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Keywords
(2)
Scalar Field
Ground State
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Nonlinear scalar field equations, I existence of a ground state
Nonlinear scalar field equations, I existence of a ground state,10.1007/BF00250555,Archive for Rational Mechanics and Analysis,H. Berestycki,P.L. Lio
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Nonlinear scalar field equations, I existence of a ground state
(
Citations: 385
)
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H. Berestycki
,
P.L. Lions
Journal:
Archive for Rational Mechanics and Analysis  ARCH RATION MECH ANAL
, vol. 82, no. 4, pp. 313345, 1983
DOI:
10.1007/BF00250555
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Citation Context
(173)
...Second, the use of Sobolev spaces of highly symmetric functions, which admit compact embeddings, as in
5
,
6
...
V. Raghavendra
,
et al.
Weak solutions for a class of semilinear elliptic equations in unbound...
...[
4
,14] and references therein, together with a vast literature that followed these works...
...In particular, it is standard to assume f is an odd function in most results on multiplicity of solutions (see [
4
,10,11] and references therein)...
...The classical result on existence of positive solution ¯ for (P∞), which is also unique, radial and decays exponentially to zero as x →∞ , due to Berestycki and Lions [
4
] will play an important role in our...
...Proof. Let ¯ ∈ N∞ be the radial positive solution of problem (P∞) given in [
4
]...
...First, we recall for instance [12 ]a nd [
4
] where it is proved there are positive constants C1 and C2 such that...
Janete S. Carvalho
,
et al.
A note on existence of antisymmetric solutions for a class of nonlinea...
...The recent mathematical literature has seen a growing interest in what we may call, borrowing a terminology from [
19
], the zero mass case of noncritical elliptic problems of the form −� u + V (x) u = g (u )i nR N ,N ≥ 3, (1.1)...
...Berestycki and Lions in [
19
], where the authors probably first used the socalled doublepower growth condition on g, namely, g (u) behaves as a subcritical power u q1−1 at infinity and a supercritical power u q2−1 near the origin, where q1 < 2 ∗ <q 2. A multiplicity result was also obtained in [20]...
Marino Badiale
,
et al.
Sum of weighted Lebesgue spaces and nonlinear elliptic equations
...The aim of this paper is to study the Schr ¨ odingerMaxwell system assuming the same very general hypotheses introduced by Berestycki & Lions, in their celebrated paper [
7
]...
...hypotheses ong are almost necessary in the sense specified in [
7
];...
...the fact that the result is obtained for small q is not surprising for at least two reasons: first, because small q makes, in some sense, less strong the influence of the term u , which constitutes, in the first equation, a perturbation with respect to the classical nonlinear Schr ¨ odinger equation treated in [
7
]; second, there is a nonexistence result for largeq andg(u) = u +jujp 1u withp2]1; 2] (see [24])...
...Following [
7
], define s0 := minfs 2 [; +1[ j g(s) = 0g (s0 = +1 if g(s)6= 0 for anys> ). We set ~ g : R! R the function such that...
...Observe that, according to [
7
], as a consequence of (g4), there exists a functionz2 H1 r (R3) such that...
Antonio Azzollini
,
et al.
On the Schrödinger–Maxwell equations under the effect of a general non...
...problem (1.1) has a positive, radially symmetric solution which tends to 0 at innity, which is usually called the ground state. We refer to [44,
4
] for a proof...
Manuel del Pino
,
et al.
The Toda system and multipleend solutions of autonomous planar ellipt...
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Citations
(385)
Weak solutions for a class of semilinear elliptic equations in unbounded domains of ℝ
V. Raghavendra
,
Rasmita Kar
Journal:
Applicable Analysis
, vol. aheadofp, no. aheadofp, pp. 19, 2012
Existence of solutions for a class of quasilinear elliptic equations in R with vanishing potentials
Qin Li
,
Zuodong Yang
Journal:
Applicable Analysis
, vol. aheadofp, no. aheadofp, pp. 113, 2012
A note on existence of antisymmetric solutions for a class of nonlinear Schrödinger equations
(
Citations: 1
)
Janete S. Carvalho
,
Liliane A. Maia
,
Olimpio H. Miyagaki
Journal:
Zeitschrift Fur Angewandte Mathematik Und Physik  ZAMP
, vol. 62, no. 1, pp. 6786, 2011
An approach to minimization under a constraint: the added mass technique
(
Citations: 1
)
Louis Jeanjean
,
Marco Squassina
Journal:
Calculus of Variations and Partial Differential Equations  CALC VAR PARTIAL DIFFER EQUAT
, vol. 41, no. 3, pp. 511534, 2011
Phytochemicals of Brassicaceae in plant protection and human health – Influences of climate, environment and agronomic practice
(
Citations: 1
)
Maria Björkman
,
Ingeborg Klingen
,
Andrew N. E. Birch
,
Atle M. Bones
,
Toby J. A. Bruce
,
Tor J. Johansen
,
Richard Meadow
,
Jørgen Mølmann
,
Randi Seljåsen
,
Lesley E. Smart
,
Derek Stewart
Journal:
Phytochemistry
, vol. 72, no. 7, pp. 538556, 2011