Bifurcation of Homoclinic Solutions for Hamiltonian Systems | Zendy

Robert Joosten | Zendy

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Bifurcation of Homoclinic Solutions for Hamiltonian Systems

Author(s) -

Robert Joosten

Publication year - 2002

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1121

Subject(s) - homoclinic orbit , homoclinic bifurcation , hamiltonian system , bifurcation , mathematics , bogdanov–takens bifurcation , mathematical physics , hamiltonian (control theory) , physics , saddle node bifurcation , mathematical optimization , nonlinear system , quantum mechanics

We consider the Hamiltonian system Ju′(x) + Mu(x)−∇uF (x, u(x)) = λu(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.

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