Hamiltonian systems of Schrodinger equations with vanishing potentials

In this paper, by means of minimax techniques involving Cerami sequences, we prove the existence of at least one pair of positive solutions for a Hamiltonian system of Schrodinger equations in R-N with potentials vanishing at infinity and subcritical nonlinearities which are superlinear at the origin and at infinity. We establish new estimates to prove the boundedness of a Cerami sequence.