Infinitely many homoclinic solutions for nonautonomous p(t)p(t)-Laplacian Hamiltonian systems

By using the Symmetric Mountain Pass Theorem, we establish some existence criteria which guarantee that the second-order ordinary p(t)p(t)-Laplacian systems of the form ddt(∣u̇(t)∣p(t)−2u̇(t))−a(t)∣u(t)∣p(t)−2u(t)+∇W(t,u(t))=0 have infinitely many homoclinic solutions, where t∈R,u∈RN, p∈C(R,R)p∈C(R,R) and p(t)>1p(t)>1, a∈C(R,R)a∈C(R,R), and W∈C1(R×RN,R)W∈C1(R×RN,R) are non-periodic in tt.