Homoclinic solutions for a nonperiodic fourth order differential equations without coercive conditions

Ziheng Zhang and Rong Yuan

Applied Mathematics and Computation, 2015, vol. 250, issue C, 280-286

Abstract: In this paper we investigate the existence of homoclinic solutions for the following fourth order nonautonomous differential equationsu(4)+wu″+a(x)u=f(x,u),(FDE)wherew is a constant, a∈C(R,R) and f∈C(R×R,R). The novelty of this paper is that, when (FDE) is nonperiodic, i.e., a and f are nonperiodic in x and assuming that a does not fulfil the coercive conditions and f satisfies some more general (AR) condition, we establish one new criterion to guarantee that (FDE) has at least one nontrivial homoclinic solution via using the Mountain Pass Theorem. Recent results in the literature are generalized and significantly improved.

Keywords: Fourth order differential equations; Homoclinic solutions; Critical point; Variational methods; Mountain Pass Theorem (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:250:y:2015:i:c:p:280-286

DOI: 10.1016/j.amc.2014.10.114

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