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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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
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bounded selfadjoint operator equations
hamiltonian systems
homoclinic orbit
indefinite second order systems
nonzero solution
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description 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.
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subjects bounded selfadjoint operator equations
hamiltonian systems
homoclinic orbit
indefinite second order systems
nonzero solution
title A nonzero solution for bounded selfadjoint operator equations and homoclinic orbits of Hamiltonian systems
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