Infinitely many homoclinic solutions for second-order Hamiltonian systems with odd nonlinearities

In this paper we study the existence of homoclinic solutions for second-order Hamiltonian systems with odd nonlinearities ü−L(t)u+Wu(t,u)=0, where L(t) and W(t,u) are not assumed to be periodic in t. We get, under certain assumptions on L and W, infinitely many homoclinic solutions for both subquadratic and superquadratic cases by using the fountain theorems in critical point theory.