Heteroclinic solutions for a class of the second order Hamiltonian systems

We shall be concerned with the existence of heteroclinic orbits for the second order Hamiltonian system , where and , V 0. We will assume that V and a certain subset satisfy the following conditions. is a set of isolated points and . For every sufficiently small ε>0 there exists δ>0 such that for all , if then −V(t,z) δ. The integrals , , are equi-bounded and −V(t,z)→∞, as t→∞, uniformly on compact subsets of . Our result states that each point in is joined to another point in by a solution of our system.