华东师范大学学报(自然科学版) ›› 2007, Vol. 2007 ›› Issue (3): 1-10.

• 数学 统计学 •    下一篇

边界层函数法在微分不等式中的应用

倪明康1, 2, 林武忠1,2   

  1. 1. 华东师范大学 数学系, 上海 200062； 2. 上海高校计算科学 E-研究院 上海交通大学研究所, 上海 200062
  • 收稿日期:2007-01-05 修回日期:2007-02-11 出版日期:2007-05-25 发布日期:2007-05-25
  • 通讯作者: 倪明康

Application of Boundary Layer Function Method in Differential Inequality(Chinese)

NI Ming-kang1, 2, LIN Wu-zhong1, 2   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062, China； 2. SJTU Section, Computational Science Division, E-Institute of Shanghai Universities, Shanghai 200030, China
  • Received:2007-01-05 Revised:2007-02-11 Online:2007-05-25 Published:2007-05-25
  • Contact: NI Ming-kang

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摘要： 针对一类常微分方程奇摄动边值问题, 介绍了用Vasil’eva\,边界层函数法来构造Nagumo定理中的上下解, 并用微分不等式证明了解的存在性和进行了余项估计. 用边界层函数法来构造上下解更具有普遍性, 且使用方便.

关键词: 奇摄动, 渐近解, 上下解, 奇摄动, 渐近解, 上下解

Abstract: This paper discussed a kind of singularly perturbed ODE with boundary value. The upper and lower solutions defined in Nagumo Theorem by means of Vasil’eva’s boundary layer function method were contructed. Actually, it is of great universality and easy to use. After the construction, the existence of the solution of this singularly perturbed problem and estimation of the remainder terms with differential estimation of inequalities
was proved.

Key words: asymptotic solution, upper and lower solutions, singular perturbation, asymptotic solution, upper and lower solutions

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