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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 4, 2002, pp. 985–1004
DOI: 10.4171/ZAA/1121

Published online: 2002-12-31

Bifurcation of Homoclinic Solutions for Hamiltonian Systems

Robert Joosten[1]

(1) Ecole Polytechnique Federale, Lausanne, Switzerland

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.

Keywords: Hamiltonian systems, homoclinic solutions, bifurcation

Joosten Robert: Bifurcation of Homoclinic Solutions for Hamiltonian Systems. Z. Anal. Anwend. 21 (2002), 985-1004. doi: 10.4171/ZAA/1121