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Existence of Homoclinic Orbits for Hamiltonian Systems with Superquadratic Potentials

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  • Jian Ding
  • Junxiang Xu
  • Fubao Zhang

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.

Suggested Citation

  • Jian Ding & Junxiang Xu & Fubao Zhang, 2009. "Existence of Homoclinic Orbits for Hamiltonian Systems with Superquadratic Potentials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    • Handle: RePEc:wly:jnlaaa:v:2009:y:2009:i:1:n:128624
    DOI: 10.1155/2009/128624
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    References listed on IDEAS

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    1. Wenming Zou & Martin Schechter, 2006. "Critical Point Theory and Its Applications," Springer Books, Springer, number 978-0-387-32968-0, March.
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