Homoclinic orbits for superquadratic Hamiltonian systems without a periodicity assumption

In this paper, we consider the second-order Hamiltonian system q̈(t)+∇V(t,q(t))=f(t) where V(t,q)=−K(t,q)+W(t,q)V(t,q)=−K(t,q)+W(t,q). Under suitable conditions on the growth of WW and KK, we establish the existence of a nontrivial homoclinic orbit without any assumption of periodicity on VV. This homoclinic orbit is obtained as a limit of solutions of a certain sequence of nil-boundary-value problems which are obtained by the minimax methods.