一类三阶非线性微分方程奇摄动两点边值问题  

Singularly Perturbed Two Points Boundary Value Problem for a Kind of Third Order Nonlinear Differential Equation

作　　者：庄红艳[1] 姚静荪[1] 吴有萍[1] 

机构地区：[1]安徽师范大学数学系,安徽芜湖241000

出　　处：《安徽工业大学学报（自然科学版）》2011年第2期197-200,共4页Journal of Anhui University of Technology（Natural Science）

基　　金：安徽省自然科学基金项目(050460103)

摘　　要：利用合成展开法研究一类非线性三阶微分方程的奇摄动边值问题,构造该问题解的高阶形式渐近展开式,用微分不等式理论证明解的存在性,并给出渐近解的误差估计,然后给出一个验证实例。Study the singularly perturbed boundary value problem for a kind of third order nonlinear differential equation by the method of composite expansion.The formal asymptotic expansion of solution is constructed,Then according to the theory of differential inequalities prove the existence of solution and get the error estimation of asymptotic solution.At last,one example is given and the result is verified.

关 键 词：奇摄动 合成展开法 微分不等式理论 

分 类 号：O175.14[理学—数学]