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 u ¨ + V u ( t , u ) = 0 , − ∞ < t < ∞ . We use variational methods under the assumption that V ( t , u ) satisfies the so-called “Strong-Force” condition.