二阶非线性时滞微分方程的奇异摄动

Singular perturbation of second order nonlinear delay differential equation

文章针对一类非线性时滞微分方程的奇异摄动边值问题,用边界层函数法构造了该问题的形式渐近解,通过构造Nagumo定理中的上下解证明了解的存在性,并进行了余项估计,得到了一致有效渐近解。

The formal asymptotic solution to the singular perturbation problem of a class of nonlinear delay dif- ferential equation is constructed by the method of boundary functions. The upper and lower solutions defined in Nagumo theorem are constructed to prove the existence of the solution of this problem. The estimation of the remainder terms is made and the uniformly valid asyrnptotic solution is given.