一类三阶非线性常微分方程的奇摄动边值问题  

Singularly perturbed BVP for a third nonlinear ODE

作　　者：陈丽华[1] 徐洁[2] 倪明康[2] 

机构地区：[1]福建师范大学福清分校数学与计算机科学系,福州350300 [2]华东师范大学数学系,上海200062

出　　处：《华东师范大学学报（自然科学版）》2008年第3期12-20,共9页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(10671070);上海市教育委员会E-研究院建设项目(E03004);地理信息科学教育部重点实验室开放课题;上海市浦江人才计划(05PJ14040)

摘　　要：利用边界层函数法研究一类非线性三阶奇摄动方程的边值问题.当gy′>0时,首先将所论问题转化成等价的Tikhonov方程组边值问题,然后构造了它的双边界层渐近解,并证明了所有边界函数的指数式衰减特性.最后给出了所论问题解的存在唯一性以及渐近解的余项估计.当gy′<0时,简要地说明了为什么本问题一般无解.This paper studied a kind of BVP of nonlinear third order singularly perturbed equations by boundary layer function method. When gy′〉0, at first, the problem was turned to a BVP of an equivalent Tikhonov system. Then the asymptotic solution of doubly boundary layer for the system was constructed, and the character of exponential decay for all boundary functions was proved. Finally the main results of this paper： existence and uniqueness of solution and estimarion of remainder for the problem were given. When gy′〈0, in general, there is no solution to this problem.

关 键 词：奇异摄动 边界函数 不变流形 渐近分析 

分 类 号：O175.14[理学—数学]