Infinitely many periodic solutions of non-autonomous second-order Hamiltonian systems

Abstract

In this paper, we study the existence of infinitely many periodic solutions for the non-autonomous second-order Hamiltonian systems with symmetry. Based on the minimax methods in critical point theory, in particular, the fountain theorem of Bartsch and the symmetric mountain pass lemma due to Kajikiya, we obtain the existence results for both the superquadratic case and the subquadratic case, which unify and sharply improve some recent results in the literature.