A Note on Homoclinic Orbits for Second Order Hamiltonian Systems
  In this paper, we study the existence for the homoclinic orbits for the second order Hamiltonian systems. Under suitable conditions on the potential $V$, we apply the direct method of variations and the Fourier analysis to prove the existence of homoclinc orbits. 
Bingyu Li and Fengying Li and Donglun Wu and Shiqing Zhang
math.DS