Existence of homoclinic solutions for a class of second-order Hamiltonian systems with general potentials

Under some local conditions on W(t,u)W(t,u), the existence of homoclinic solutions is obtained for the nonperiodic second-order Hamiltonian systems ü(t)−L(t)u(t)+∇W(t,u(t))=f(t) as a limit of periodic solutions of a certain sequence of boundary-value problems which are obtained by a new critical point theorem.