Existence of Homoclinic Orbits for Hamiltonian Systems with Superquadratic Potentials

Jian Ding, Junxiang Xu and Fubao Zhang

Abstract and Applied Analysis, 2009, vol. 2009, issue 1

Abstract: This paper concerns solutions for the Hamiltonian system: z˙=𝒥Hz(t,z). Here H(t, z) = (1/2)z · Lz + W(t, z), L is a 2N × 2N symmetric matrix, and W ∈ C1(ℝ × ℝ2N, ℝ). We consider the case that 0 ∈ σc(−(𝒥(d/dt) + L)) and W satisfies some superquadratic condition different from the type of Ambrosetti‐Rabinowitz. We study this problem by virtue of some weak linking theorem recently developed and prove the existence of homoclinic orbits.

Date: 2009
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https://doi.org/10.1155/2009/128624

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2009:y:2009:i:1:n:128624

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