非线性边值条件非线性方程的奇摄动问题  

Singularly perturbed problem for nonlinear equation with nonlinear boundary value condition

作　　者：纪明亮[1] 李青[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：《高校应用数学学报（A辑）》2013年第2期171-179,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10901103);安徽高校省级自然科学基金(KJ2011A135)

摘　　要：研究了三阶非线性边值条件的非线性方程奇摄动问题,先用合成展开法对形式近似解进行构造,再利用相关微分不等式理论给出所得解的存在性及一致有效性的证明.Singulary perturbed problem for third-order nonlinear equation with nonlinear boundary value condition is considered.Using the method of composite expansion,the formal asymptotic expansion of solution of the problem is constructed.Then using the theory of differential inequalities, the existence of solution and the uniformly validity of the expansion are proved.

关 键 词：奇摄动 非线性 边值条件 渐近解 

分 类 号：O175.14[理学—数学]