Open AccessA nonzero solution for bounded selfadjoint operator equations and homoclinic orbits of Hamiltonian systems
Author(s) -
Mei Song,
Runzhen Li
Publication year - 2021
Publication title -
electronic journal on the qualitative theory of differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.524
H-Index - 33
ISSN - 1417-3875
DOI - 10.14232/ejqtde.2021.1.68
Subject(s) - homoclinic orbit , bounded function , mathematics , hamiltonian system , heteroclinic orbit , hamiltonian (control theory) , mountain pass theorem , operator (biology) , class (philosophy) , pure mathematics , orbit (dynamics) , mathematical analysis , mathematical physics , physics , nonlinear system , quantum mechanics , bifurcation , computer science , mathematical optimization , biochemistry , chemistry , repressor , artificial intelligence , transcription factor , gene , engineering , aerospace engineering
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.