Homoclinic Orbits for a Singular Second Order Planar Hamiltonian System

The existence of a homoclinic orbit for a singular second order planarHamiltonian system is proved by using variational methods. The main assumptions are the strong force condition and the uniqueness of a global maximum of a singular potential. The functional corresponding to the approximate problem satisfies the Palais-Smale compactness condition and attains its infimum. Solutions of this approximate problem are obtained as minimal points of the fanctional. The homoclinic orbit is the limit of these solutions.