用两个重要方法处理一类奇摄动问题

摘要

本论文主要讨论了奇摄动常微分方程、非局部椭圆型方程的边值问题和奇摄动非局部反应扩散问题的解的存在性及渐近性态。在已构造出奇摄动问题形式渐近解的基础上,运用微分不等式和不动点原理证明原问题的形式渐近解的一致有效性。值得指出的是在2.1通过微分不等式方法讨论了二阶奇摄动常微分方程非线性边界条件；在2.2将双参数问题引入到偏微分方程中，并得到相应结果；并且考虑了常微分方程、偏微分方程中的非局部问题。

目录

CHAPTER 1. Introduction

CHAPTER 2. The singular perturbation problems dealt with the theory of differential inequalities

2.1 A CLASS OF SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEM FOR INTEGRAL DIFFERENTIAL EQUATIONS

2.2 A CLASS OF SINGULARLY PERTURBED NONLOCAL REACTION DIFFUSION EQUATIONS INVOLVING TWO PARAMETERS

2.3 A CLASS OF SINGULARLY PERTURBED SEMILINEAR ELLIPTIC EQUATIONS

CHAPTER 3. The singular perturbation problems dealt with by the fixed point principle

3.1 SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM FOR SECOND ORDER NONLINEAR EQUATION

3.2 NONLOCAL PROBLEM FOR SINGULARLY PERTURBED ELLIPTIC EQUATIONS

REFERENCES

ACKNOWLEDGEMENTS

The papers published or to appear