A nonzero solution for bounded selfadjoint operator equations and homoclinic orbits of Hamiltonian systems

We obtain an existence theorem of nonzero solution for a class of bounded selfadjoint operator equations. The main result contains as a special case the existence result of a nontrivial homoclinic orbit of a class of Hamiltonian systems by Coti Zelati, Ekeland and Séré. We also investigate the exist...

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Bibliographic Details
Published in:Electronic journal of qualitative theory of differential equations 2021-01, Vol.2021 (68), p.1-13
Main Authors: Song, Mingliang, Li, Runzhen
Format: Article
Language:English
Subjects:
bounded selfadjoint operator equations
hamiltonian systems
homoclinic orbit
indefinite second order systems
nonzero solution
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Summary:We obtain an existence theorem of nonzero solution for a class of bounded selfadjoint operator equations. The main result contains as a special case the existence result of a nontrivial homoclinic orbit of a class of Hamiltonian systems by Coti Zelati, Ekeland and Séré. We also investigate the existence of nontrivial homoclinic orbit of indefinite second order systems as another application of the theorem.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2021.1.68