Article ID Journal Published Year Pages File Type
4627196 Applied Mathematics and Computation 2015 7 Pages PDF
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)a∈C(R,R) and f∈C(R×R,R)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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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