Analysis of a Singularly-Perturbed Linear Two-Point Boundary-Value Problem

摘要

This paper presents a simple constructive proof of the existence of solutions to a class of singularly-perturbed linear two-point boundary-value problems. Such problems arise when detailed models for physical phenomena involve effects that occur on markedly different temporal or spatial scales, the (singularly) small parameter measuring the disparity between the scales. This simple constructive proof, through slight modification, also allows one to prove the existence of solutions of a class of finite difference schemes used to approximate the solution of the continuous problem. Keywords: Differential equations; Greens function.