In this paper, we consider the differential-operator equation View the MathML source Turn MathJax on with A a self-adjoint unbounded operator coefficient, which does not have a fixed sign. The Cauchy problem for the equation above with conditions of the form View the MathML source Turn MathJax on is known to be an ill-posed problem. In this ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 409, no. 1, 2014]]>In this paper we consider the strong asymptotic behavior of Laguerre polynomials in the complex plane. The leading behavior is well known from Perron and Mehler–Heine formulas, but higher order coefficients, which are important in the context of Krall–Laguerre or Laguerre–Sobolev-type orthogonal polynomials, are notoriously difficult to compute. In this paper, we propose the use of ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 403, no. 2, pp. 477-486, 2013]]>In this paper, we investigate a non-iterative imaging algorithm based on the topological derivative in order to retrieve the shape of penetrable electromagnetic inclusions when their dielectric permittivity and/or magnetic permeability differ from those in the embedding (homogeneous) space. The main objective is the imaging of crack-like thin inclusions, but the algorithm can be applied to arbitrarily ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 402, no. 2, 2013]]>Here, it is observe that ΛBV (p) (; B), the class of functions of bounded p−Λ− variation from a non-empty compact subset of R into a com- mutative unital Banach algebra B, is a commutative unital Banach algebra. Moreover, (Λ 1 ;:::; Λ N ) BV (p) (Π N=1 i;B), the class of N −variables functions of bounded p−(Λ ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 4, no. 1, 2012]]>Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 389, 2012]]>

The new notion of slice monogenic functions introduced in the paper [F. Colombo, I. Sabadini, D.C. Struppa, Slice monogenic functions, Israel J. Math. 171 (2009) 385–403] led us to define a new functional calculus for an n-tuple of not necessarily commuting operators, see [F. Colombo, I. Sabadini, D.C. Struppa, A new functional calculus for noncommuting operators, ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 2, pp. 655-679, 2011]]>The boundedness character of positive solutions of the following max-type difference equationxn=max{A,xn−1pxn−kr},n∈N0, where k∈N∖{1}, the parameters A and r are positive and p is a nonnegative real number is studied in this paper. Our main results considerably improve results appearing in the literature.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 376, no. 1, pp. 317-328, 2011]]>In this paper we develop the multilevel augmentation method for solving nonlinear operator equations of the second kind and apply it to solving the one-dimensional sine-Gordon equation. We first give a general setting of the multilevel augmentation method for solving the second kind nonlinear operator equations and prove that the multilevel augmentation method preserves the optimal convergence order ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 375, no. 2, pp. 706-724, 2011]]>Computable bounds for the generalized complete elliptic integrals of the first and second kind are obtained. Also, bounds for some combinations and products for integrals under discussion are established. It has been proven that both families of integrals are logarithmically convex as functions of the first parameter. This property has been employed to obtain several inequalities involving integrals in question.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 1, pp. 203-213, 2011]]>By using the Symmetric Mountain Pass Theorem, we establish some existence criteria to guarantee the second-order self-adjoint discrete Hamiltonian system Δ[p(n)Δu(n−1)]−L(n)u(n)+∇W(n,u(n))=0 has infinitely many homoclinic orbits, where n∈Z, u∈RN, p,L:Z→RN×N and W:Z×RN→R are no periodic in n. Our conditions on the potential ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 1, pp. 59-72, 2011]]>Let A be a unilateral (resp., bilateral) weighted shift with weights wn, n⩾0 (resp., −∞n∞). Eckstein and Rácz showed before that A has its numerical range W(A) contained in the closed unit disc if and only if there is a sequence {an}n=0∞ (resp., {an}n=−∞∞) in [−1,1] such that |wn|2=(1−an)(1+an+1) for all...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 381, no. 2, pp. 897-909, 2011]]>Hermitian Clifford analysis is a higher dimensional function theory centered around the simultaneous null solutions, called Hermitian monogenic functions, of two Hermitian conjugate complex Dirac operators. As an essential step towards the construction of an orthogonal basis of Hermitian monogenic polynomials, in this paper a Cauchy–Kovalevskaya extension theorem is established for such polynomials. The minimal number of initial polynomials ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 381, no. 2, pp. 649-660, 2011]]>We consider initial value/boundary value problems for fractional diffusion-wave equation: ∂tαu(x,t)=Lu(x,t), where 0α⩽2, where L is a symmetric uniformly elliptic operator with t-independent smooth coefficients. First we establish the unique existence of the weak solution and the asymptotic behavior as the time t goes to ∞ and the proofs are based on ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 382, no. 1, pp. 426-447, 2011]]>In this work we study, in the framework of Colombeauʼs generalized functions, the Hamilton–Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 382, no. 1, pp. 487-502, 2011]]>In this paper we consider the Gibbs measure on the one-sided shift dynamical system and determine the quantization dimension function for the image measure supported on a Moran set. A relationship between the quantization dimension function and the temperature function of the thermodynamic formalism arising in multifractal analysis is also established.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 1, pp. 73-82, 2011]]>This paper studies two widely used stochastic non-autonomous logistic models. For the first system, sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The critical number between weak persistence and extinction is obtained. For the second system, sufficient criteria for extinction, non-persistence in the mean, weak persistence in the mean, strong ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 375, no. 2, pp. 443-457, 2011]]>In this paper, the invertibility of nonnegative Hamiltonian operator with unbounded entries is studied, and the sufficient conditions for the everywhere defined bounded invertibility of nonnegative Hamiltonian operator are obtained.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 2, pp. 410-413, 2011]]>The eccentric distance sum is a novel topological index that offers a vast potential for structure activity/property relationships. For a graph G, it is defined as ξd(G)=∑v∈Vε(v)D(v), where ε(v) is the eccentricity of the vertex v and D(v)=∑u∈V(G)d(u,v) is the sum of all distances from the vertex ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 381, no. 2, pp. 590-600, 2011]]>The Lambert W function is shown to be the Laplace exponent of a positive infinitely divisible law (i.e. W is a Bernstein function) called the standard Lambert law. This law is a generalized gamma convolution. At least three Poisson mixture families are defined in terms of W. One of these is the generalized Poisson laws which are shown to ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 378, no. 2, pp. 480-492, 2011]]>We undertake a thorough investigation of the moments of Ramanujanʼs alternative elliptic integrals and of related hypergeometric functions. Along the way we are able to give some surprising closed forms for Catalan-related constants and various new hypergeometric identities.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 384, no. 2, pp. 478-496, 2011]]>In this paper, a mathematical model for tumor growth with time delay in proliferation under indirect effect of inhibitor is studied. The delay represents the time taken for cells to undergo mitosis. Nonnegativity of solutions is investigated. The steady-state analysis is presented with respect to the magnitude of the delay. Existence of Hopf bifurcation is proved for some parameter ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 374, no. 1, pp. 178-186, 2011]]>We prove that every biorthogonality preserving linear surjection between two dual or compact C⁎-algebras or between two von Neumann algebras is automatically continuous.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 376, no. 1, pp. 221-230, 2011]]>We obtain a criterion for the quasi-regularity of generalized (non-sectorial) Dirichlet forms, which extends the result of P.J. Fitzsimmons on the quasi-regularity of (sectorial) semi-Dirichlet forms. Given the right (Markov) process associated to a semi-Dirichlet form, we present sufficient conditions for a second right process to be a standard one, having the same state ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 384, no. 1, pp. 33-48, 2011]]>In this paper three-dimensional superradiance problem is considered and a differential operator that commutes with the integral operator related to the problem is obtained. All the eigenfunctions of the differential operator are found and a complete set of eigensolutions for the three-dimensional superradiance problem is obtained.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 375, no. 2, pp. 762-776, 2011]]>We study Li–Yorke chaos and distributional chaos for operators on Banach spaces. More precisely, we characterize Li–Yorke chaos in terms of the existence of irregular vectors. Sufficient “computable” criteria for distributional and Li–Yorke chaos are given, together with the existence of dense scrambled sets under some additional conditions. We also obtain certain spectral properties. Finally, we show ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 1, pp. 83-93, 2011]]>In this paper, we study growth and zeros of linear difference equationsPn(z)f(z+n)+⋯+P1(z)f(z+1)+P0(z)f(z)=F(z) where F(z),Pn(z),…,P0(z) are polynomials with FPnP0≢0 and satisfy deg(Pn+⋯+P0)=max{degPj:j=0,…,n}⩾1. The corresponding homogeneous equation of the above equation is also investigated.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 1, pp. 235-241, 2011]]>This paper derives relations between the following properties of a C∗-algebra: (i) it has the fpp, (ii) the spectrum of every self-adjoint element is finite, (iii) it is finite dimensional, (iv) it is generated by two projections p and q and the spectrum of p+q is homeomorphic to a compact ordinal αωω, (v) it is generated by two ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 374, no. 1, pp. 22-28, 2011]]>In finance, many option pricing models generalizing the Black–Scholes model do not have closed form, analytic solutions so that it is hard to compute the solutions or at least it requires much time to compute the solutions. Therefore, asymptotic representation of options prices of various type has important practical implications in finance. This paper presents asymptotic expansions of option ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 375, no. 2, pp. 490-501, 2011]]>A function f:Vn→W, where V is a commutative semigroup, W is a linear space and n⩾1 is an integer, is called multi-additive if it is additive in each variable. In this paper we prove the generalized Hyers–Ulam stability of multi-additive mappings in non-Archimedean normed spaces, using the so-called direct method.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 2, pp. 376-383, 2011]]>In this paper we are concerned with the study of a nonstandard quasi-hemivariational inequality. Using a fixed point theorem for set-valued mappings the existence of at least one solution in bounded closed and convex subsets is established. We also provide sufficient conditions for which our inequality possesses solutions in the case of unbounded sets. Finally, the uniqueness and ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 1, pp. 305-315, 2011]]>The simultaneous null solutions of the two complex Hermitian Dirac operators are focused on in Hermitian Clifford analysis, where the Hermitian Cauchy integral was constructed and will play an important role in the framework of circulant (2×2) matrix functions. Under this setting we will present the half Dirichlet problem for circulant (2×2) matrix functions on the unit ball of even ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 374, no. 2, pp. 442-457, 2011]]>Marcinkiewicz–Zygmund laws with convergence rates are established here for a class of strictly stationary ergodic sequences.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 375, no. 2, pp. 738-744, 2011]]>Analyzing several classical tests for convergence/divergence of number series, we relax the monotonicity assumption for the sequence of terms of the series. We verify the sharpness of the obtained results on corresponding classes of sequences and functions.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 377, no. 1, pp. 194-206, 2011]]>Given a second-order elliptic operator on Rd, with bounded diffusion coefficients and unbounded drift, which is the generator of a strongly continuous semigroup on L2(Rd) represented by an integral, we study the time behavior of the integral kernel and prove estimates on its decay at infinity. If the diffusion coefficients are symmetric, a local lower estimate is also ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 377, no. 1, pp. 170-179, 2011]]>In this paper, the maximal operator associated with multilinear Calderón–Zygmund singular integral operators will be studied by using an improved Coltlar's inequality. Moreover, weighted norm inequalities and some estimates on weighted Hardy spaces are obtained for this maximal operator.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 2, pp. 384-392, 2011]]>We consider the existence of multiple positive solutions to the steady state reaction diffusion equation with Dirichlet boundary conditions of the form:{−Δu=λ[u−u2K−cu21+u2],x∈Ω,u=0,x∈∂Ω. Here Δu=div(∇u) is the Laplacian of u, 1λ is the diffusion coefficient, K and c are positive constants and Ω⊂RN is a smooth bounded region with ∂Ω in C2. ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 381, no. 2, pp. 732-741, 2011]]>We solve the following three questions concerning surjective linear isometries between spaces of Lipschitz functions Lip(X,E) and Lip(Y,F), for strictly convex normed spaces E and F and metric spaces X and Y:(i)Characterize those base spaces X and Y for which all isometries are weighted composition maps.(ii)Give a condition independent of base spaces ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 377, no. 1, pp. 15-29, 2011]]>Let ϕA be a normal completely positive map on B(H) with Kraus operators {Ai}i=1∞. Denote M the subset of normal completely positive maps by M={ϕA:∑i=1∞AiAi⁎⩽I,∑i=1∞Ai⁎Ai⩽I and ϕA is normal}. In this note, the relations between the fixed points of ϕA and ϕA† are investigated. We obtain that {B∈K(H):ϕA(B)=B}={...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 382, no. 1, pp. 172-179, 2011]]>Let E be a separable Fréchet space. The operators T1,…,Tm are disjoint hypercyclic if there exists x∈E such that the orbit of (x,…,x) under (T1,…,Tm) is dense in E×⋯×E. We show that every separable Banach space E admits an m-tuple of bounded linear operators which are disjoint hypercyclic. If, in addition, its dual...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 374, no. 1, pp. 106-117, 2011]]>It has been treated as a difficult problem to find iterative roots of non-monotonic functions. For some PM functions which do not increase the number of forts under iteration a method was given to obtain a non-monotonic iterative root by extending a monotone iterative root from the characteristic interval. In this paper we prove that every continuous iterative ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 378, no. 1, pp. 359-373, 2011]]>In this paper we prove monotone convergence theorems for Henstock–Kurzweil integrable functions from a compact real interval to an ordered Banach space. These theorems are then applied to prove existence results for solutions of a discontinuous functional integral equation containing Henstock–Kurzweil integrable functions.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 377, no. 1, pp. 286-295, 2011]]>We study the weighted Fermat–Torricelli (w.F-T) problem for geodesic triangles on a C2 complete surface and on an Aleksandrov space of curvature bounded above by a real number K and solve an “inverse” problem on a C2 complete surface. The solution of the w.F-T problem and the inverse w.F-T problem on a C2 ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 1, pp. 44-58, 2011]]>We prove a uniqueness theorem in terms of value distribution for meromorphic solutions of a class of nonlinear partial differential equations of first order, which shows that such solutions f are uniquely determined by the zeros and poles of f−cj (counting multiplicities) for two distinct complex numbers c1 and c2.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 377, no. 2, pp. 881-888, 2011]]>By establishing a proper variational framework and using the critical point theory, we establish some new existence criteria to guarantee the 2nth-order nonlinear difference equation containing both many advances and retardationsΔn(r(t−n)Δnu(t−n))+q(t)u(t)=f(t,u(t+n),…,u(t),…,u(t−n)),n∈Z(3),t∈Z, has at least one or infinitely many ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 381, no. 2, pp. 485-505, 2011]]>A family of compact and positively invariant sets with uniformly bounded fractal dimension which at a uniform exponential rate pullback attract bounded subsets of the phase space under the process is constructed. The existence of such a family, called a pullback exponential attractor, is proved for a nonautonomous semilinear abstract parabolic Cauchy problem. Specific examples will be presented in the ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 381, no. 2, pp. 748-765, 2011]]>In this article k-convex metric spaces are considered where a several variable mapping is provided as a limit point of an iteration scheme based on the midpoint map in the metric space itself. This mapping, considered as a mean of its variables, has some properties which relates it to the center of mass of these variables in the metric ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 381, no. 1, pp. 383-391, 2011]]>We consider the compressible Navier–Stokes–Korteweg system that models the motions of the compressible isothermal viscous capillary fluids. We prove the optimal L2 and Lp, p⩾2 decay rates for the classical solutions and their spatial derivatives. In particular, the optimal L2 decay rate of the second-order spatial derivatives is obtained. The proof is based on the detailed study ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 379, no. 1, pp. 256-271, 2011]]>An existence result of three non-zero solutions for non-autonomous elliptic Dirichlet problems, under suitable assumptions on the nonlinear term, is presented. The approach is based on a recent three critical points theorem for differentiable functionals.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 382, no. 1, pp. 1-8, 2011]]>We consider a process (Xt(α))t∈[0,T) given by the SDE dXt(α)=αb(t)Xt(α)dt+σ(t)dBt, t∈[0,T), with initial condition X0(α)=0, where T∈(0,∞], α∈R, (Bt)t∈[0,T) is a standard Wiener process, b:[0,T)→R∖{0} and σ:[0,T)→(0,∞) are continuously differentiable ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 380, no. 2, pp. 405-424, 2011]]>In the present paper we consider the trigonometric series with (β,r)-general monotone and (β,r)-rest bounded variation coefficients. Necessary and sufficient conditions of L-convergence for such series are obtained in terms of the coefficients. Moreover, we generalize and extend the Tikhonov results [J. Math. Anal. Appl. 347 (2008) 416–427] to the class GM(β,r) ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 2, pp. 449-463, 2011]]>We obtain existence and localization results of positive nontrivial solutions for a class of semilinear elliptic variational systems. The proof is based on variants of Schechter's localized critical point theorems for Hilbert spaces not identified to their duals and on the technique of inverse-positive matrices. The Leray–Schauder boundary condition is also involved.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 1, pp. 138-146, 2011]]>In the paper an internal geometric characterization of strongly starlike mappings of order alpha in Cn is given.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 375, no. 2, pp. 538-542, 2011]]>We study the Neumann boundary stabilization problem of a coupled transport-diffusion system in the case where the observation is done at the boundary. In the recent paper of Sano and Nakagiri [H. Sano, S. Nakagiri, Stabilization of a coupled transport-diffusion system with boundary input, J. Math. Anal. Appl. 363 (2010) 57–72], we treated the stabilization problem for ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 377, no. 2, pp. 807-816, 2011]]>We discuss the solvability of the following strongly nonlinear BVP:{(a(x(t))Φ(x′(t)))′=f(t,x(t),x′(t)),t∈R,x(−∞)=α,x(+∞)=β where αβ, Φ:(−r,r)→R is a general increasing homeomorphism with bounded domain (singular Φ-Laplacian), a is a positive, continuous function and f is a Carathéodory nonlinear function....

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 378, no. 2, pp. 667-679, 2011]]>It is shown that a curve q(t), t∈I (0∈I) of idempotent operators on a Banach space X, which verifies that for each ξ∈X, the map t↦q(t)ξ∈X is continuously differentiable, can be lifted by means of a regular curve Gt, of invertible operators in X:q(t)=Gtq(0)Gt−1,t∈I. This is done by using the transport ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 378, no. 1, pp. 252-267, 2011]]>Deterministic descriptions of three biochemical reaction channels formerly considered by Bratsun et al. (2005) [19] are studied. These descriptions are based on the mass action law and for the simple protein production with delayed degradation differ from that proposed by Bratsun et al. An explicit solution to this model is calculated. For the model of reaction with negative feedback and ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 376, no. 1, pp. 74-83, 2011]]>The existence of a pullback exponential attractor being a family of compact and positively invariant sets with a uniform bound on their fractal dimension which at a uniform exponential rate pullback attract bounded subsets of the phase space under the evolution process is proved for the nonautonomous logistic equation and a system of reaction–diffusion equations with time-dependent external ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 381, no. 2, pp. 766-780, 2011]]>For functions from the Sobolev space Hs(Ω), 12s32, definitions of non-unique generalized and unique canonical co-normal derivative are considered, which are related to possible extensions of a partial differential operator and its right-hand side from the domain Ω, where they are prescribed, to the domain boundary, where they are not. Revision of the boundary value problem ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 378, no. 1, pp. 324-342, 2011]]>We present a new characterization of minimizing sequences and possible minimizers (all called the minimizing magnetizations) for a nonlocal micromagnetic-like energy (without the exchange energy). Our method is to replace the nonlocal energy functional and its relaxation with certain local integral functionals on divergence-free fields obtained by a two-step minimization of some auxiliary augmented functionals. Through this ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 374, no. 1, pp. 230-243, 2011]]>In this paper, we study the existence and multiplicity of homoclinic orbits for a class of first-order nonperiodic Hamiltonian systems. By applying two recent critical point theorems for strongly indefinite functionals, we give some new criteria to guarantee that Hamiltonian systems with asymptotically quadratic terms and spectrum point zero have at least one and a finite number of pairs ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 378, no. 1, pp. 117-127, 2011]]>In this paper, the initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation over an open bounded domain G×(0,T), G∈Rn are considered. Based on an appropriate maximum principle that is formulated and proved in the paper, too, some a priory estimates for the solution and then its uniqueness are established. To show the existence ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 374, no. 2, pp. 538-548, 2011]]>J.R. Holub (1988) [10] introduced the concept of backward shift on Banach spaces. We show that an infinite-dimensional function algebra does not admit a backward shift. Moreover, we define a backward quasi-shift as a weak type of a backward shift, and show that a function algebra A does not admit it, under the assumption that the Choquet ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 377, no. 1, pp. 135-144, 2011]]>In this note, we consider the quasilinear elliptic equation ±Δpu=h(x)um+H(x)un in RN (N⩾3), where 0m⩽p−1n. We establish conditions sufficient to ensure the nonexistence of nonnegative entire solutions, which improves a result of A.V. Lair [A.V. Lair, Large solutions of mixed sublinear–superlinear elliptic equations, J. Math. Anal. Appl. 346 (2008) 99–106].

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 379, no. 1, pp. 8-14, 2011]]>Let S={Si}i∈I be an arbitrary family of complex n-by-n matrices, where 1⩽n∞. Let ρˆ(S) denote the joint spectral radius of S, defined asρˆ(S)=lim supℓ→+∞{sup(i1,…,iℓ)∈Iℓ‖Si1⋯Siℓ‖1/ℓ}, which is independent of the norm ‖⋅‖ used here. A semi-norm ‖⋅‖⁎ on Cn is called “extremal” of S, if it satisfies‖x‖⁎≢0and‖x⋅Si‖⁎⩽ρˆ(S)...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 379, no. 2, pp. 827-833, 2011]]>Fix strictly increasing right continuous functions with left limits and periodic increments, Wi:R→R, i=1,…,d, and let W(x)=∑i=1dWi(xi) for x∈Rd. We construct the W-Sobolev spaces, which consist of functions f having weak generalized gradients ∇Wf=(∂W1f,…,∂Wdf). Several properties, that are analogous to classical results on Sobolev spaces, are obtained. Existence ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 382, no. 1, pp. 214-230, 2011]]>It was recently proven in Case et al. (2010) [2] that, under mild restrictions, grad-div stabilized Taylor–Hood solutions of Navier–Stokes problems converge to the Scott–Vogelius solution of that same problem. However, even though the analytical rate was only shown to be γ−12 (where γ is the stabilization parameter), the computational results suggest the rate may be ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 381, no. 2, pp. 612-626, 2011]]>In this paper, our main aim is to introduce the concept of planar p-harmonic mappings and investigate the properties of these mappings. First, we discuss the p-harmonic Bloch mappings. Two estimates on the Bloch constant are obtained, which are generalizations of the main results in Colonna (1989) [9]. As a consequence of these investigations, we establish a Bloch ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 1, pp. 102-110, 2011]]>A one-parameter family of variational problems is examined that interpolates between torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. The associated partial differential equation is derived, which is shown to have positive solutions in many cases. Results are obtained regarding extremal domains and regarding variations of the domain or the parameter.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 379, no. 2, pp. 818-826, 2011]]>The quantization dimension function for a probability measure induced by a set of infinite contractive similarity mappings and a given probability vector is determined. A relationship between the quantization dimension function and the temperature function of the thermodynamic formalism arising in multifractal analysis is established. The result in this paper is an infinite extension of Graf and Luschgy [S. Graf, ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 383, no. 2, pp. 499-505, 2011]]>By employing majorant functions, the existence and uniqueness of holomorphic solutions to nonlinear fractional partial differential equations (the Cauchy problems) are introduced. Furthermore, the analytic continuation of solutions is studied.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 380, no. 1, pp. 232-240, 2011]]>We obtain some results on generalized Hyers–Ulam stability of the linear differential equation in a Banach space. As a consequence we improve some known estimates of the difference between the perturbed and the exact solutions.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 381, no. 2, pp. 530-537, 2011]]>We continue to investigate the connection between the spectrum of self-adjoint ordinary differential operators with arbitrary deficiency index d and the number of linearly independent square-integrable solutions for real values of the spectral parameter λ. We show that if, for all λ in an open interval I, there are d linearly independent square-integrable solutions, then there is ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 376, no. 2, pp. 696-712, 2011]]>We are concerned with an infinite dimensional variational inequality which is connected with the dynamic oligopolistic market equilibrium problem. We will provide existence theorems and show, under minimal assumptions on the data, the Lipschitz continuity of the solution. Moreover a general duality theory is provided overcoming the difficulty of the voidness of the interior of the ordering cone which defines ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 382, no. 1, pp. 231-247, 2011]]>Comparison arguments are applied to derive decreasing sequences of upper solutions and increasing sequences of lower solutions for a class of nonlinear elliptic equations. The monotonicity of the two sequences is proven. These polynomial sequences are obtained by applying new algorithms and solving linear differential equations. The obtained upper and lower solutions are analytic and have closed forms. Different examples ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 374, no. 2, pp. 402-411, 2011]]>Let G be a graph and f:G→G be a continuous map. Denote by P(f), R(f) and Ω(f) the sets of periodic points, recurrent points and non-wandering points of f, respectively. In this paper we show that: (1) If L=(x,y) is an open arc contained in an edge of G such that {fm(x),...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 383, no. 2, pp. 553-559, 2011]]>We present a proof of the existence of solutions to the continuous coagulation equation with multiple fragmentation whenever the kernels satisfy certain growth conditions. The proof relies on weak L1 compactness methods applied to suitably chosen approximating equations. The question of uniqueness is also considered.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 374, no. 1, pp. 71-87, 2011]]>The authors of this paper study the existence and uniqueness of weak solutions of the initial and boundary value problem for ut=div((uσ+d0)|∇u|p(x,t)−2∇u)+f(x,t). Localization property of weak solutions is also discussed.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 374, no. 2, pp. 374-384, 2011]]>This paper deals with the Keller–Segel model{ut=Δu−χ∇⋅(u∇v),x∈Ω,t>0,vt=Δv−uv,x∈Ω,t>0, under homogeneous Neumann boundary conditions in a smooth bounded domain Ω⊂Rn, n⩾2, with nonnegative initial data (u(⋅,0),v(⋅,0))∈(W1,r(Ω))2 (for some r>n), ‖u(⋅,0)‖L1(Ω)>0 ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 381, no. 2, pp. 521-529, 2011]]>We propose a new approach to the multiple-scale analysis of difference equations, in the context of the finite operator calculus. We derive the transformation formulae that map any given dynamical system, continuous or discrete, into a rescaled discrete system, by generalizing a classical result due to Jordan. Under suitable analytical hypotheses on the function space we consider, the rescaled ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 376, no. 1, pp. 247-258, 2011]]>We give a new solvability criterion for the boundary Carathéodory–Fejér problem: given a point x∈R and, a finite set of target values, to construct a function f in the Pick class such that the first few derivatives of f take on the prescribed target values at x. We also derive a linear fractional parametrization of the set of solution...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 382, no. 2, pp. 645-662, 2011]]>Let K be the scalar field of real numbers or complex numbers and L0(F,K) the algebra of equivalence classes of K-valued random variables defined on a probability space (Ω,F,P). In this paper, we first characterize the algebraic structure of finitely generated L0(F,K)-modules and then combining the recently developed separation theorem in random ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 381, no. 2, pp. 833-842, 2011]]>We deal with the probabilistic approach to a nonlinear operator Λ of the form Λu=Δu+∑k=1∞qkuk, in connection with the works of M. Nagasawa, N. Ikeda, S. Watanabe, and M.L. Silverstein on the discrete branching processes. Instead of the Laplace operator we may consider the generator of a right (Markov) process, called base process, with a general (not ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 384, no. 1, pp. 16-32, 2011]]>Let B=B1(0) be the unit ball in Rn and r=|x|. We study the poly-harmonic Dirichlet problem{(−Δ)mu=f(u)in B,u=∂u∂r=⋯=∂m−1u∂rm−1=0on ∂B.Using the corresponding integral equation and the method of moving planes in integral forms, we show that the positive solutions are radially symmetric and monotone decreasing about the ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 377, no. 2, pp. 744-753, 2011]]>Countable projective limits of countable inductive limits, called PLB-spaces, of weighted Banach spaces of continuous functions have recently been investigated by Agethen, Bierstedt and Bonet. We extend their investigation to the case of holomorphic functions regarding the same type of questions, i.e. we analyze locally convex properties in terms of the defining double sequence of weights and study ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 383, no. 2, pp. 409-422, 2011]]>For continuous self-maps of compact metric spaces, we study the syndetically proximal relation, and in particular we identify certain sufficient conditions for the syndetically proximal cell of each point to be small. We show that any interval map f with positive topological entropy has a syndetically scrambled Cantor set, and an uncountable syndetically scrambled set invariant under some power ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 379, no. 2, pp. 656-663, 2011]]>This paper studies exponential stabilization of distributed semilinear systems. The paper (i) gives a constrained feedback control that ensure the exponential stabilizability and (ii) shows that this control is the unique solution of an appropriate minimization problem. Examples of hyperbolic partial equations are provided.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 380, no. 1, pp. 117-123, 2011]]>For the complex differential equationf(n)+An−1(z)f(n−1)+⋯+A1(z)f′+A0(z)f=0 with analytic coefficients Aj in the unit disk, our contribution is to build up a relationship between the coefficients and solutions of the equation. We provide conditions for coefficients Aj such that all solutions of the equation belong to the QK spaces.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 375, no. 2, pp. 478-489, 2011]]>In this paper we study the Cauchy problem of the Debye system for initial data in the Lorentz space Ln,1(Rn) and the Besov space B˙Ln,1,∞−α(Rn) for 0α1. Some local existence theorems are proved.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 383, no. 2, pp. 337-343, 2011]]>The Proper Generalized Decomposition (PGD) is a methodology initially proposed for the solution of partial differential equations (PDE) defined in tensor product spaces. It consists in constructing a separated representation of the solution of a given PDE. In this paper we consider the mathematical analysis of this framework for a larger class of problems in an abstract setting. In particular, ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 376, no. 2, pp. 469-480, 2011]]>We consider in this paper the problem of asymptotic behavior of solutions to an abstract linear dissipative integrodifferential equation with infinite memory (past history) modeling linear viscoelasticity. We show that the stability of the system holds for a much larger class of the convolution kernels than the one considered in the literature, and we provide a relation between the decay ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 382, no. 2, pp. 748-760, 2011]]>In this paper, we establish some new Lyapunov type inequalities for second-order half-linear differential equations, which almost generalize and extend all related existing results in the literature.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 382, no. 2, pp. 792-801, 2011]]>The aim of the paper is to present a new approach to the theory of functional integral equations of fractional order. That approach depends on converting of the mentioned equations to the form of functional integral equations of Volterra–Stieltjes type. It turns out that the study of functional integral equations of Volterra–Stieltjes type is more convenient and effective ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 375, no. 2, pp. 375-387, 2011]]>In this paper we study properties of complex symmetric operators. In particular, we prove that every complex symmetric operator having property (β) or (δ) is decomposable. Moreover, we show that complex symmetric operator T has Dunfordʼs property (C) and it satisfies Weylʼs theorem if and only if its adjoint does.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 379, no. 1, pp. 325-333, 2011]]>In this paper, we establish several new Lyapunov type inequalities for linear Hamiltonian systems on an arbitrary time scale T when the end-points are not necessarily usual zeroes, but rather, generalized zeroes, which generalize and improve all related existing ones including the continuous and discrete cases.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 381, no. 2, pp. 695-705, 2011]]>In this paper, we study the existence of infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems. By using the variant fountain theorem, we obtain a new criterion for guaranteeing that second-order Hamiltonian systems has infinitely many homoclinic solutions. Recent results from the literature are generalized and significantly improved. An example is also given in ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 373, no. 1, pp. 20-29, 2011]]>We consider the Schwarz-type boundary-value problem (BVP) of the nonhomogeneous Cauchy–Riemann equation on an isosceles orthogonal triangle. By the technique of plane parqueting and the Cauchy–Pompeiu formula on the triangle, the Schwarz–Poisson formula is obtained. We also investigate boundary behaviors of the Schwarz-type operator and the Pompeiu-type operator. Especially, boundary-values at the ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 377, no. 2, pp. 557-570, 2011]]>In this paper, we prove the existence of infinitely many quasiperiodic solutions for a class of coupled Duffing-type equations via KAM theorem. Moreover, the set of quasiperiodic solutions is of infinitely Lebesgue measure in the phase space.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 374, no. 2, pp. 429-441, 2011]]>Despite the availability of treatment that is effective, Trichomonas vaginalis infections are still high. A deterministic model for transmission dynamics of Trichomonas vaginalis is presented as a system of non-linear differential equations. Analysis of the reproduction number has shown that an increase in the number of straight women (non-lesbians) infected result in an increase in the number of ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 379, no. 2, pp. 852-860, 2011]]>This paper gives a group of expansion formulas for the inertias of Hermitian matrix polynomials A−A2, I−A2 and A−A3 through some congruence transformations for block matrices, where A is a Hermitian matrix. Then, the paper derives various expansion formulas for the ranks and inertias of some matrix pencils generated from two or three orthogonal projectors and Hermitian unitary matrices. As ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 376, no. 1, pp. 162-186, 2011]]>The study of a very large class of linear and non-linear, stationary and evolutive partial differential problems in the half-space (or similar) under the slip boundary condition is reduced here to the much simpler study of the corresponding results for the same problem in the whole space. The approach is particularly suitable for proving new results in strong ...

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 377, no. 1, pp. 216-227, 2011]]>