EXISTENCE OF SUBHARMONIC SOLUTIONS FOR NON-AUTONOMOUS SECOND ORDER HAMILTONIAN SYSTEMS UNDER SOME WEAK CONDITIONS

Abstract

In the present paper, we study that under some weak conditions, the following non-autonomous second order Hamiltonian systems

\ddot{u}(t) + \nabla F(t, u(t)) = 0 a. e. t \in R

have infinitely distinct subharmonic solutions. The results in this paper develop and generalize some recent results.