JournalszaaVol. 21, No. 4pp. 985–1004

Bifurcation of Homoclinic Solutions for Hamiltonian Systems

  • Robert Joosten

    Ecole Polytechnique Federale, Lausanne, Switzerland
Bifurcation of Homoclinic Solutions for Hamiltonian Systems cover
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Abstract

We consider the Hamiltonian system

Ju(x)+Mu(x)uF(x,u(x))=λu(x).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 FF. We study both the case where FF is defined globally with respect to uu and the case where FF 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