两参数奇摄动非线性椭圆型方程Robin边值问题的广义解  

Generalized solution of the singularly perturbed robin boundary value problems for nonlinear elliptic equation with two parameters

作　　者：汪维刚 陈贤峰[2] 温朝晖[3] 莫嘉琪[4] 

机构地区：[1]安庆师范学院桐城教学部,安徽桐城231402 [2]上海交通大学,上海200240 [3]安徽财经大学统计与应用数学学院应用数学研究所,安徽蚌埠233030 [4]安徽师范大学数学系,安徽芜湖241003

出　　处：《西北大学学报（自然科学版）》2014年第5期719-723,共5页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11371248);安徽高校自然科学基金资助项目(KJ2013A133;KJ2014A151)

摘　　要：研究了一类奇摄动椭圆型方程Robin边值问题。在适当的条件下,利用泛函分析理论,摄动方法引入伸长变量,分别构造了问题的外部解和边界层校正项,并得到了原问题形式渐近解。最后利用微分不等式理论和不动点定理,证明了问题广义解的存在性。并且得到了解的一致有效的渐近展开式。The singularly perturbed Robin boundary value problem for a class of nonlinear elliptic equation is studied. Under the suitable conditions, the formal asymptotic solution is obtained using the theory of functional analysis, perturbation method and introducing the stretched variables, the outer solution and boundary layer correction terms of the problem are constructed respectively. And the formal asymptotic solution of the original problem is found. Finally, the existence of generalized solution for the problem is proved using the singular perturbation method and fixed theorem. And the uniformly valid asymptotic expression of the solution is obtained.

关 键 词：非线性 ROBIN问题 奇异摄动 

分 类 号：O175.29[理学—数学]