具有局部弱稳定退化解二阶非线性方程的奇摄动问题  

Singular Perturbation Problems of Second-Order Nonlinear Equations with Locally Weak Stable Reduced Solutions

作　　者：秦赵娜[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：《吉林大学学报（理学版）》2013年第5期819-825,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11201004);安徽省高校自然科学基金重点项目(批准号:KJ2011A135)

摘　　要：讨论一类二阶非线性方程奇摄动Dirichlet问题的边界层现象,在退化解是局部弱稳定的假设下,利用界定函数法和微分不等式理论证明了呈边界层性态解的存在性,并给出了解的渐近估计.The authors studied boundary layer phenomena for some singularly perturbed Diriehlet problems of second-order nonlinear equations. Under the principal assumption that a reduced solution is locally weak stable, the existence of solution which exhibits boundary layer behavior was proved via the method of bounding functions and the theory of clifferential inequality, with the asymptotic estimation of solution given.

关 键 词：奇摄动 非线性方程 局部弱稳定 微分不等式 

分 类 号：O175.14[理学—数学]