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

The 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.