A unified approach to periodic solutions for a class of non-autonomous second order Hamiltonian systems

Abstract

This paper is dedicated to studying the periodic solutions of non-autonomous second order Hamiltonian systems. By virtue of control functions and the minimax methods in critical point theory, we propose a unified approach when the nonlinearity is unbounded while grows no more than |x| at infinity. We establish some new existence theorems on periodic solutions, which unify and generalize many previously known results in the literature.