On a class of singular second-order Hamiltonian systems with infinitely many homoclinic solutions

Abstract

We show existence of infinitely many homoclinic orbits at the origin for a class of singular second-order Hamiltonian systems $$\ddot{u}+V_u(t,u)=0,-\infty <t<\infty .$$ We use variational methods under the assumption that\ $V(t,u)$\ satisfies the so-called "Strong-Force" condition.