Homoclinic orbits for an infinite dimensional Hamiltonian system with periodic potential

Abstract

In this paper, we study the following diffusion system Open image in new window where \(z:(u,v):\mathbb{R}\times\mathbb{R}^{N}\rightarrow\mathbb{R}^{2}\), \(V(x)\in C(\mathbb{R}^{N},\mathbb{R})\) is a general periodic function, g(t,x,v), f(t,x,u) are periodic in t,x and superquadratic in v,u at infinity. By using much more direct methods to prove all Cerami sequences for the energy functional are bounded and establish the existence of homoclinic orbits, which are ground state solutions for above system.