Existence and Multiplicity Results for Heteroclinic Orbits of Second Order Hamiltonian Systems

Connecting orbits of nonlinear differential equations have long been studied in the dynamical systems literature, generally in a setting involving perturbations and using a Melnikov function. In this article, we consider a class of second order Hamiltonian systems which possess infinitely many or finite number of equilibria. Using variational arguments and penalization methods, we obtain the existence of multiple heteroclinic orbits joining pairs of equilibria.