Multiple homoclinic solutions for superquadratic Hamiltonian systems

In this article we study the existence of infinitely many homoclinic solutions for a class of second-order Hamiltonian systems $$ \ddot{u}-L(t)u+W_u(t,u)=0, \quad \forall t\in\mathbb{R}, $$ where L is not required to be either uniformly positive definite or coercive, and W is superquadratic at infinity in u but does not need to satisfy the Ambrosetti-Rabinowitz superquadratic condition