homoclinic orbits for superquadratic hamiltonian systems without a periodicity assumption

in this paper, we consider the second-order hamiltonian system ¨q(t)+∇v(t, q(t)) = f (t) where v(t, q) = −k(t, q) + w(t, q). under suitable conditions on the growth of w and k, we establish the existence of a nontrivial homoclinic orbit without any assumption of periodicity on v. this homoclinic orbit is obtained as a limit of solutions of a certain sequence of nil-boundary-value problems which are obtained by the minimax methods.