Infinitely many homoclinic solutions for a second-order Hamiltonian system with locally defined potentials

Xiaoping Wang

Chaos, Solitons & Fractals, 2016, vol. 87, issue C, 47-50

Abstract: In this paper, we study homoclinic solutions of the following second-order Hamiltonian system u¨(t)−L(t)u(t)+∇W(t,u(t))=0,where t∈R,u∈RN,L:R→RN×N and W:R×RN→R. Applying a new symmetric Mountain Pass Theorem established by Kajikiya, we prove the existence of infinitely many homoclinic solutions for the above system in the case where L(t) is coercive but unnecessarily positive definite for all t∈R, and W(t, x) is only locally defined near the origin with respect to x. Our results significantly generalize and improve related ones in the literature.

Keywords: Homoclinic solution; Hamiltonian system; Symmetric Mountain Pass Theorem (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:87:y:2016:i:c:p:47-50

DOI: 10.1016/j.chaos.2016.02.034

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