关键词: 非线性, 奇摄动, 初值问题, 渐近解, 边界层

Abstract: A class of initial value problems for nonlinear differentialdifference equation with small time delay was studied with the corrective method of boundary layer. Under some definite conditions, the uniformly valid a symptotic solution of the problems was obtained. Especially, two corrective terms of boundary layer were given. They are decreasing continuously and exponentially and have the characteristic of ladder structure.

Key words: nonlinear, singular perturbation, initial value problem, asymptotic solution, boundary layer