华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (5): 60-65.

• 应用数学与基础数学 • 上一篇    下一篇

一类脉冲微分方程的渐近解

武利猛 1, 倪明康 1,2, 陆海波 1, 郑 艳 1   

  1. 1. 华东师范大学 数学系, 上海 200241; 2. 上海高校计算科学E-研究院 上海交通大学研究所, 上海 200240
  • 收稿日期:2011-02-01 修回日期:2011-05-01 出版日期:2011-09-25 发布日期:2011-11-22

Asymptotic solution for a class of impulsive differential equations

WU Li-meng 1, NI Ming-kang 1,2, LU Hai-bo 1, ZHENG Yan 1   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200241, China; 2. Division of Computational Science, E-Institute of Shanghai Universities, SJTU, Shanghai 200240, China
  • Received:2011-02-01 Revised:2011-05-01 Online:2011-09-25 Published:2011-11-22

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摘要： 研究一类含有单个脉冲点的脉冲微分方程. 基于奇摄动理论, 通过分步法, 将原脉冲微分方程问题扩充为奇摄动问题, 证明了扩充问题的解是原问题解很好的近似, 从而为进一步研究脉冲微分方程问题提供了新途径. 其次, 利用边界层函数法, 构造了原问题连续的形式渐近解, 证明了解的存在性和进行了余项估计. 最后, 通过例子验证了主要结果.

关键词: 奇摄动, 渐近解, 脉冲微分方程

Abstract: By means of singular perturbation theory, We constructed the singularly perturbed problem for the impulsive differential equation problem, and proved that the solution of the derived problem approximated to the solution of original problem, indicating a new way for the study of impulsive differential equations. By virtue of boundary function method, we not only constructed
continuous formal asymptotic solution but also proved the existence of solution, meanwhile the remainder estimate was presented. Finally, an example was given to illustrate the results.

Key words: singular perturbation, asymptotic solution, impulsive differential equation

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