Homoclinic solutions for a class of second-order Hamiltonian systems

Some new results for the existence of homoclinic orbits are obtained for the second-order Hamiltonian systems ü(t)+∇V(t,u(t))=f(t), where t∈R,u∈Rnt∈R,u∈Rn and V∈C1(R×Rn,R)V∈C1(R×Rn,R), V(t,x)=−K(t,x)+W(t,x)V(t,x)=−K(t,x)+W(t,x) is TT-periodic with respect to tt, T>0T>0 and f:R→Rnf:R→Rn is a continuous and bounded function. Our assumptions on KK and ff are rather loose.