Bifurcation of Homoclinic Solutions for Hamiltonian Systems

Abstract

We consider the Hamiltonian system

Using variational methods obtained by Stuart on the one hand and by Giacomoni and Jeanjean on the other, we get bifurcation results for homoclinic solutions by imposing conditions on the function $F$. We study both the case where $F$ is defined globally with respect to $u$ and the case where $F$ is defined locally only.