Periodic solutions for Hamiltonian systems without Ambrosetti-Rabinowitz condition and spectrum 0

In this paper, we consider the superquadratic second order Hamiltonian system u ''(t) + A(t)u(t) + del H (t, u(t)) = 0, t is an element of R. Our main results here allow the classical Ambrosetti-Rabinowitz superlinear condition to be replaced by a general superquadratic condition, and 0 lies in a gap of sigma (B), where B := - d(2)/dt(2) - A(t). We will study the ground state periodic solutions for this problem. The main idea here lies in an application of a variant generalized weak linking theorem for strongly indefinite problem developed by Schechter and Zou. (C) 2011 Elsevier Inc. All rights reserved.