非线性边值条件三阶非线性方程的奇摄动  

Singularly perturbed problem for third-order nonlinear equation with nonlinear boundary value conditions

作　　者：李青[1] 纪明亮[1] 姚静荪[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241003

出　　处：《应用数学与计算数学学报》2012年第4期423-432,共10页Communication on Applied Mathematics and Computation

基　　金：安徽高校省级自然科学基金资助项目(KJ2011A135)

摘　　要：研究了一类具非线性边值条件的三阶非线性方程的奇摄动问题,选用非常规的渐近序列和合成展开法构造形式渐近解,并用微分不等式理论证明了所得渐近解的一致有效性.The singularly perturbed problem for the third-order nonlinear equation with nonlinear boundary value conditions is considered. Using the unconventional asymptotic sequence and the method of the composite expansion, the formal asymptotic expansion of the solution to the problem is constructed. By using the theory of differential inequalities, the existence of the solution and the uniform validity of the expansion are proved.

关 键 词：奇摄动 非线性方程 非线性边值条件 

分 类 号：O175[理学—数学]