Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential

A new existence result of homoclinic orbits is obtained for the second-order Hamiltonian systems u ¨ ( t ) = ∇ F ( t , u ( t ) ) + f ( t ) , where F ( t , x ) is periodic with respect to t. This result generalizes some known results in the literature.