Homoclinic solutions for a second-order Hamiltonian system with a positive semi-definite matrix

Juntao Sun and Tsung-fang Wu

Chaos, Solitons & Fractals, 2015, vol. 76, issue C, 24-31

Abstract: In this paper, we study homoclinic solutions for second-order Hamiltonian systems u¨-L(t)u+Wu(t,u)=0, where L(t) is allowed to be a positive semi-definite symmetric matrix for all t∈R, and W∈C1(R×RN,R) is an indefinite potential satisfying asymptotically quadratic condition at infinity on u. We obtain some new results on the existence and multiplicity of homoclinic solutions for second-order systems. The proof is based on variational methods.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:76:y:2015:i:c:p:24-31

DOI: 10.1016/j.chaos.2015.03.004

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