New existence and multiplicity results of homoclinic orbits for a class of second order Hamiltonian systems

Yiwei Ye and Chun-Lei Tang

Chaos, Solitons & Fractals, 2014, vol. 69, issue C, 151-159

Abstract: In this paper, we study the nonperiodic second order Hamiltonian systemsu¨(t)-λL(t)u(t)+∇W(t,u(t))=0,∀t∈R,where λ⩾1 is a parameter, the matrix L(t) is not necessarily positive definite for all t∈R nor coercive. Replacing the Ambrosetti–Rabinowitz condition by general superquadratic assumptions, we establish the existence and multiplicity results for the above system when λ>1 large. We also consider the situation where W is a combination of subquadratic and superquadratic terms, and obtain infinitely many homoclinic solutions.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:69:y:2014:i:c:p:151-159

DOI: 10.1016/j.chaos.2014.09.016

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