Existence of Homoclinic Orbits for Hamiltonian Systems with Superquadratic Potentials

This paper concerns solutions for the Hamiltonian system: (z) over dot = partial derivative H-z(t, z). Here H(t, z) = (1/2)z . Lz + W(t, z), L is a 2Nx 2N symmetric matrix, and W is an element of C-1(R x R-2N, R). We consider the case that 0 is an element of sigma(c) (-(partial derivative (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. Copyright (C) 2009 Jian Ding et al.