New existence of homoclinic orbits for a second-order Hamiltonian system

By using the Mountain Pass Theorem and the Symmetric Mountain Pass Theorem, we establish some existence criteria to guarantee that the second-order Hamiltonian system ü(t)−a(t)|u(t)|p−2u(t)+∇W(t,u(t))=0 has at least one or infinitely many homoclinic orbits, where t∈R,u∈RN, a∈C(R,R)a∈C(R,R) and W∈C1(R×RN,R)W∈C1(R×RN,R) are not periodic in tt. Our conditions on the potential W(t,x)W(t,x) are rather relaxed.