几类二阶方程的奇摄动问题的研究.pdfVIP

证明了该问题在一定条件下呈边界层和角层性态的解的存在性，并给出了解的渐近估 计 . 关 键 i司：奇摄动；非线性方程；边值问题；微分不等式理论；不动点定理 主 题 分 类 ( A M S 2000): 34B15, 34E15 2 万方数据 Study on Several C lasses of Singular P erturbation of Second-order Equations A b st r a c t In this thesis, boundary layer and inner layer phenomena for several cla es of singularly perturbed problems are studied by the method of bounding functions and the method of composite expansion. The existence of solutions for the original prob­ lems are proved and the asymptotic estimation of solutions are given using the theory of differential inequality or the improved fixed point theorem. The basic structure of this paper is as follow ： In the first chapter, we describe the research significance and situation of singular perturbed problems, introduce some research results of the boundary layer and the inner layer phenomena related to this paper. Then we present the main work and the innovation of this paper. In the second chapter, we construct the upper and lower solutions of a cla of singularly perturbed problems for second-order semi-linear differential equations with nonlinear and infinitely-large boundary value condition ^ y = f (t ，y )， a t b， A — g ( y ( a ) ，y (a)) = - ，h ( y ( b ) ，y (b))= - by comparison equation. Then the existence of the solutions for the problems i proved and the asymptotic estimate of solutions is given by the theory of differential inequality. Finally, two examples are given to illustrate the si