非线性奇摄动Robin边值问题解的渐近分析

Asymptotic Analysis of a Nonlinear Singularly Perturbed Robin Boundary Value Problem

本文用间接的方法证明了一类非线性奇摄动方程组的Ｒｏｂｉｎ问题解的存在唯一性，给出解对ε任意精确度的一致有效展开，并把结果推广到更一般的边值条件。

An indirect proof of existence and uniqueness is given for solutions of the Robin problem for the singularly perturbed nonlinear equation system in this paper. A proposed asymptotic expantion of a solution,as provided by the Vasileva construction,is uniformly available throughout the entire compact interval. Meanwile,this paper also extends the result to a general boundary-value condition subject to a certain assumption.