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

Abstract

Under some local conditions on W ( t , u ) , the existence of homoclinic solutions is obtained for the nonperiodic second-order Hamiltonian systems u ̈ ( 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.