具非线性边界条件的Volterra型泛函微分方程边值问题奇摄动

首先利用微分不等式理论和一些分析技巧，探讨了一类具非线性边界条件的二阶Volterra型泛函微分方程边值问题解的存在性问题，然后通过对右端边界层函数和外部解的构造，进一步研究了一类具小参数的二阶Votterra型非线性边值问题，利用微分中值定理和上、下解方法得到了边值问题解的存在性，并给出了解的关于小参数的一致有效渐近展开式。

Singularly Perturbed Nonlinear Boundary Value Problem for a Kind of Volterra Type Functional Differential Equation

By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second order Volterra functional differential equation was considered first. Then, by constructing the right_side layer function and the outer solution, a nonlinear boundary value problem subject to a kind of second order Volterra functional differential equation with a small parameter was studied further. By using the differential mean value theorem and the technique of upper and lower solution, a new result on the existence of the solutions to the boundary value problem is obtained, and a uniformly valid asymptotic expansions of the solution is given as well.