Homoclinic solutions for a class of second-order Hamiltonian systems

A new result for existence of homoclinic orbits is obtained for the second-order Hamiltonian systems u ¨ ( t ) − L ( t ) u ( t ) + ∇ [ W 1 ( t , u ( t ) ) − W 2 ( t , u ( t ) ) ] = f ( t ) , where t ∈ R , u ∈ R n and W 1 , W 2 ∈ C 1 ( R × R n , R ) and f ∈ C ( R , R n ) are not necessary periodic in t. This result generalizes and improves some existing results in the literature.