# Bifurcation of Homoclinic Solutions for Hamiltonian Systems

### Robert Joosten

Ecole Polytechnique Federale, Lausanne, Switzerland

## Abstract

We consider the Hamiltonian system

$Ju'(x) + Mu(x) – \bigtriangledown _u F(x,u(x)) = \lambda u(x).$

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.

## Cite this article

Robert Joosten, Bifurcation of Homoclinic Solutions for Hamiltonian Systems. Z. Anal. Anwend. 21 (2002), no. 4, pp. 985–1004

DOI 10.4171/ZAA/1121