ON EXISTENCE OF PERIODIC AND SUBHARMONIC SOLUTIONS WITH SADDLE POINT CHARACTER

Abstract

In the present paper we consider the existences of periodic and subharmonic solutions with saddle point character for the following second order non-autonomous Hamiltonian system
{\"u}(t) + \nabla F(t, u(t)) = 0 a, e, t in R.
Adopting some other reasonable assumptions for \nabla F, we obtain some new results for existence of solutions with saddle point character by using of the saddle point reduction methods. Recent results from the literature are generalized and significantly improved.