On a class of singular boundary value problems with singular perturbation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Xie, Feng

关键词: Singular boundary value problem;    Singular perturbations;    Lower and upper solutions;    Existence and uniqueness;    Asymptotic estimate;   

DOI  :  10.1016/j.jde.2011.10.003

来源: Elsevier

【 摘 要 】

In this paper we investigate a class of singular second order differential equations with singular perturbation subject to three-point boundary value conditions, whose solution exhibits a couple of boundary layers at two endpoints. We first establish a lower-upper solutions theorem by using the Schauder fixed point theorem. By the asymptotic expansions and the lower-upper solutions theorem we obtain the existence, asymptotic estimates and uniqueness for the proposed problem. Several examples are given for illustrating our results. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free