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

摘要

In this paper, we consider the superquadratic second order Hamiltonian system. 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 σ(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.