Homoclinic solutions for a class of nonperiodic and noneven second-order Hamiltonian systems

AbstractThe existence of homoclinic solutions is obtained for second-order Hamiltonian systems −u¨(t)+L(t)u(t)=∇W(t,u(t))−f(t), as the limit of the solutions of a sequence of nil-boundary-value problems which are obtained by the Mountain Pass theorem, when L(t) and W(t,x) are neither periodic nor even with respect to t