一类奇摄动三阶拟线性边值问题的渐近解  

Asymptotic Solution of Singularly Perturbed Boundary Value Problem for the Third Order Quasilinear Equation

作　　者：许进[1] 林乐义[1] 

机构地区：[1]河海大学文天学院基础部,安徽马鞍山243031

出　　处：《大学数学》2016年第2期12-16,共5页College Mathematics

基　　金：河海大学文天学院校级自然科学课题(WT15007)

摘　　要：研究了一类具有边界层性质的三阶拟线性奇摄动边值问题.在适当的条件下,用合成展开法构造出该问题的形式近似式,并应用改进的不动点定理证明了解的存在性及其渐近性质.A class of the third-order quasilinear singularly perturbed boundary value problem with boundary layer properties is studied. Under the appropriate conditions, the formal approximation of the problem is constructed by using the method of composite expansions, and the existence and asymptotic behavior of the solution are proved by the improvement of the fixed point theorem.

关 键 词：奇摄动 边值问题 边界层 合成展开法 不动点定理 逆算子定理 

分 类 号：O175.14[理学—数学]