Volterra型积分微分方程非线性边值问题

Nonlinear Boundary Value Problems for Integro-differential Equations of Volterrs Type

本文首先利用上、下解方法研究了一类Ｖｏｌｔｅｒｔａ型积分微分方程Ｄｉｒｉｃｈｌｅｔ问题和非线性边值问题的解的存在性；然后，利用所得到的微分不等式理论考虑一类相应的奇摄动非线性边值问题，获得包括边界层在内的一致有效渐近解的存在性。

In this paper we first discuss the existence of solutions of Dirichlet and nonlinear bound-ary value problems for a class of Volterra integro-differential equations by using upper andlower solutions, Then, by virtue of differential inequalities obtained,we consider a classof corresponding singularly perturbed nonlinear boundary value problem,and obtain theexistence of uniformly valid asymptotic solution involving boundary layer。