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

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