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Existence of homoclinic solutions for a class of second-order Hamiltonian systems

Existence of homoclinic solutions for a class of second-order Hamiltonian systems,10.1016/j.na.2009.06.073,Nonlinear Analysis-theory Methods & Applica

Existence of homoclinic solutions for a class of second-order Hamiltonian systems   (Citations: 3)
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A new result for existence of homoclinic orbits is obtained for the second-order Hamiltonian systems under a class of new superquadratic conditions. A homoclinic orbit is obtained as a limit of solutions of a certain sequence of boundary-value problems which are obtained by the minimax methods.
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    • ...(AR) is the so-called global Ambrosetti–Rabinowitz condition (see e.g., [3]), which implies that W (t, q) is superquadratic as |q |→ +∞ .A ssuming that (L) and (AR) hold and introducing some compact embedding theorem, Omana and Willem [16] showed that the (PS) condition is satisfied and obtained the existence and multiplicity of homoclinic solutions of (HS) using the usual Mountain Pass Theorem, which has been improved in recent paper [ ...

    Rong Yuanet al. Homoclinic Solutions for a Class of Second Order Hamiltonian Systems

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