一类具有边界和内部点摄动的非线性问题(英文)  

A Class of Nonlinear Problems With Perturbation Both in Boundary and Interior Points

作　　者：唐荣荣[1] 

机构地区：[1]湖州师范学院理学院,湖州浙江313000

出　　处：《数学进展》2013年第1期89-94,共6页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.11071205);the Natural Science Foundation of Zhejiang Province(No.Y6090164)

摘　　要：在适当的条件下,用边界摄动理论和微分不等式技巧,研究了一类摄动不仅发生在方程而且同时发生在内部点和边界处的非线性奇摄动问题.利用改进以往相关文献中辅助函数的构造证明了解的存在性,得到了原问题解以及解的导函数的任意阶一致有效渐近表达式.本文的结果丰富和推广了相关成果.Under appropriate conditions, using the boundary perturbation theory and the technique of differential inequalities, a class of nonlinear singularly perturbed problems with perturbation not only arising in the equation but also arising in interior points and boundary points is considered. The existence of solution is proved by improving the structure of auxiliary functions in the literature. The uniformly valid asymptotic expansion of the solution and its derivation for arbitrary order are obtained. The conclusion in this paper richens and improves some early results.

关 键 词：非线性问题 奇异摄动 微分不等式 渐近性态 

分 类 号：O175.14[理学—数学]