HOMOCLINIC SOLUTIONS FOR A CLASS OF SECOND ORDER HAMILTONIAN SYSTEMS WITH LOCALLY DEFINED SUBQUADRATIC POTENTIALS

Abstract

In this paper, we study the existence of infinitely many homoclinic solutions for a class of subquadratic second order Hamiltonian systems with locally defined potentials. By using a critical point theorem related to the symmetric mountain pass lemma, two new criteria for guaranteeing that the systems have infinitely many homoclinic solutions which converge to zero. Recent results in the literature are generalized and significantly improved.