MULTIPLE SOLUTIONS FOR HAMILTONIAN SYSTEMS WITH PERIODIC NONLINEARITY AND STRONG RESONANCE

§ I. Introduction In this paper we are looking for solutions of the following Hamiltonian system of second order: where x= (x_1, x_2) and V satisfies (V. 1) V: R×R~2→R is a C~1-function, 1-periodic In t, (V.2) V is periodic in x_1 with the period T>0, (V. 3) V→O, V_x→O as |x_2|→∞, uniformly in (t, x_1).