Infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems

Abstract

In this paper, we mainly consider the existence of infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems $\ddot{u}-L(t)u+W_u(t,u)=0$, where $L(t)$ is not necessarily positive definite and the growth rate of potential function $W$ can be in $(1,3/2)$. Using the variant fountain theorem, we obtain the existence of infinitely many homoclinic solutions for the second-order Hamiltonian systems.