Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4627196 | Applied Mathematics and Computation | 2015 | 7 Pages |
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
Authors
Ziheng Zhang, Rong Yuan,