二阶非线性奇摄动泛函微分方程边值问题

Boundary Value Problem of The Second Order Nonlinear Singular Perturbed Functional Differential Equation

在本文中，考虑一类抽象泛函微分方程奇摄动边值问题。这里f(t,x,ε)≥m>0.g:[0,1]×R×C（[-r,0],R）×[01]→R是连续泛函。在适当的假设了，证明了上述问题的退化问题在[0，1]上有唯一的解一和解的存在唯一性，得到了解的渐近展歼式。

In this paPer, we conider a class of boundary value problems of the abstract functional dif-feretial equations Where f(t,x,ε)≥m>0.g:[0,1]×R×C([-r,0],R)×[0,1]→R is a continous func-tional. Under the suitable conditions,existence and uniqueness of the soution of the problem and its reduced problem has been proved. Then, the asynptOtic exPansion of the solution of the probem is obtained and its uniformly valid is proved as well.