Abstract : we consider a singularly perturbed boundary value problem for higher order semilinear elliptic equation . using the comparison theorem , the uniform validity of the asymptotic solution is proved 文摘:本文研究了一类高阶半线性椭圆型方程奇摄动边值问题.利用比较定理，证明了渐近解的致有效性
Using the matching asymptotic expanding method , the solutions for a class of nonliear singularly perturbed problems are discussed . zero order asymptotic expansions of solution for boundary value problem are obtain 摘要利用匹配渐近展开法，讨论了一类非线性奇摄动问题的解，得出了奇摄动边值问题的零次渐近展开式。
What is worth pointing out is that by applying the fixed point theorem , a class of boundary value problems for singularly perturbed ordinary differential equations which are very difficulty to deal with by using the method of differential equalities are studied 值得指出的是，本文用不动点原理研究了一类用微分不等式方法难以处理的奇摄动常微分方程的边值问题。
In this dissertation , the existence and asymptotic behavior of solutions for boundary value problems of singularly perturbed ordinary differential equations and elliptic equations as well as singularly perturbed reaction diffusion problems are mainly considered 本论文主要讨论了奇摄动常微分方程、椭圆型方程的边值问题和奇摄动反应扩散问题的解的存在性及渐近性态。
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 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。
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 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 paper , these two methods are employed to consider three kinds of singular perturbation boundary value problems . in the first section , the existence of solution for a class of non - linear systems with three - point boundary problem is obtained by applying the differential inequality theory . in the second section , we use the differential inequality theory to discuss the non - monotone interior layer solution for one kind of singularly perturbed quasilinear boundary value problems with a turning point . in the third section , the diagonalization method is applied to study the existence of solution for a class of vector differential systems with two - point or three - point boundary problems . meanwhile , the asymptotic estimate of the solution as well as its first - order derivative and its second - order derivative is obtained 在第一部分中，我们应用微分不等式理论证明了一类非线性系统三点边值问题解的存在性；在第二部分中，运用微分不等式理论研究了一类带有转向点的拟线性奇摄动边值问题的非单调内层解；在第三部分中，利用对角化方法研究了一类向量二点或者三点边值问题解的存在性，并获得解及它的一、二阶导数的渐近估计。
By using the asymptotic analysis method and the diagonalization technique , considers the singular perturbation of boundary value problem for system of third order nonlinear integro - differential equation . under appropriate assumptions , the existence of the solution of perturbation problem has been proved and a asymptotic expansion of the solution and the estimation of the corresponding remainder term are geven as well 研究三阶非线性积分微分方程组边值问题的奇摄动.在适当的条件下，利用渐近分析方法和对角化技巧，证得解的存在性并给出解的渐近展开式及其余项估计
This paper studies the corner layer behavior in quasi linear systems with turning points . under the appropriate conditions and by usin g the theory of differential inequality , the existence of the solution and its c omponentwise uniformly valid asymptotic estimation are obtained when the reduced solution does not have a continuous first - derivative in some point of ( 0 , 1 ) 奇摄动转向点问题是来自量子力学及其他物理力学中的重要问题，特别对非线性系统的转向点问题，已有的结果甚少，文章研究一类具有转向点的拟线性系统的角层现象，在适当的假设条件下，利用微分不等式方法证明了当其退化解在( 0 ， 1 )内某些点上一阶导数不连续时解的存在性，并得到了解的按分量的一致有效的渐近估计。
