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