具有多参数的奇摄动非线性边值问题的摄动解  

Singularly perturbed solution for nonlinear equations with some parameters

作　　者：李超[1] 王晓云[2] 

机构地区：[1]中北大学理学院,山西太原030051 [2]山西警官高等专科学校基础部,山西太原030021

出　　处：《纯粹数学与应用数学》2012年第3期370-377,共8页Pure and Applied Mathematics

基　　金：山西省自然科学基金(2011011002-1);中国博士后科学基金(20100471857)

摘　　要：讨论含多个参数的高阶非线性方程的摄动解,在适当的条件下,先构造出外部解,再根据不同的边界层,利用伸展变量和幂级数展开式理论,构造问题的形式渐近解,最后利用微分不等式理论证明渐近解的一致有效性和渐近形态,把奇摄动非线性问题中的参数推广到多个参数.A class of nonlinear speed system perturbed solution nonlocal problem is discussed in this paper. In appropriate conditions, first constructed out external solution,again according to different boundary layer and using stretchy variable and power series launched theory, the asymptotic expansions of solution of this problem is shown and proved to be uniformly effective using the theory of differential inequality in the whole interval. This paper extends the perturbed problem of the parameters of the parameters of the promotion to multiple parameters.

关 键 词：非线性 多参数 奇摄动 边值问题 边界层校正 

分 类 号：O178[理学—数学]