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

作　　者：周津[1] 程燕[2] 

机构地区：[1]陆军军官学院研究生管理大队,安徽合肥230031 [2]陆军军官学院基础部,安徽合肥230031

出　　处：《合肥工业大学学报（自然科学版）》2013年第4期483-485,共3页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(41175058)

摘　　要：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.

关 键 词：奇摄动 时滞微分方程 渐近解 

分 类 号：O175.14[理学—数学]