On a class of singular boundary value problems with singular perturbation

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.