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。
In this dissertation, the existence and asymptotic behavior of solutions for boundary value problems of singularly perturbed ordinary differential equations and nonlocal elliptic equations as well as singularly perturbed reaction diffusion problems are mainly considered. On the basis of the formal asymptotic solutions having been constructed for the singularly perturbed problems, the formal asymptotic solutions for the original problems are proved by using the differential inequalities and the fixed point theorems. What is worth pointing out is that in 2.1 a class of singularly perturbed second order ordinary differential equations with nonlinear boundary value condi- tions are discussed by using the method of differential inequalities; In 2.2 introduce two small parameters into partial differential equations and obtain the result accordingly; What's more, consider nonlocal problem for ordinary and partial differential equations.
引文
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