Abstract and Applied Analysis
Volume 2009 (2009), Article ID 128624, 15 pages
doi:10.1155/2009/128624
Research Article

Existence of Homoclinic Orbits for Hamiltonian Systems with Superquadratic Potentials

Jian Ding, Junxiang Xu, and Fubao Zhang

Department of Mathematics, Southeast University, Nanjing 210018, China

Received 20 September 2009; Revised 19 November 2009; Accepted 6 December 2009

Academic Editor: Stephen Clark

Copyright © 2009 Jian Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.