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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2016, Vol. 33 ›› Issue (1): 106-110.doi: 10.3969/j.issn.1005-3085.2016.01.010

• • 上一篇    

一阶时滞微分方程正周期解的存在性问题(英)

翁爱治   

  1. 上海政法学院经济管理学院，上海 201701
  • 收稿日期:2014-10-29 接受日期:2015-06-29 出版日期:2016-02-15 发布日期:2016-04-15
  • 基金资助:
    上海市科学技术委员会基金 (13ZR1444500)；上海政法大学基金 (sz12015).

Positive Periodic Solutions of First-order Delay Differential Equations

WENG Ai-zhi   

  1. Department of Economics and Management, Shanghai University of Political Science and Law, Shanghai 201701
  • Received:2014-10-29 Accepted:2015-06-29 Online:2016-02-15 Published:2016-04-15
  • Supported by:
    The Committee of Science and Technology of Shanghai (13ZR1444500); the Shanghai University of Political Science and Law (sz12015).

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摘要： 本文研究一类一阶时滞微分方程正周期解的存在性问题，该类微分方程经线性化后可能是退化的．众所周知，大部分研究周期解存在性的方法都只适用于方程是非退化的情况．针对该问题，本文利用Schauder不动点定理给出周期解存在的定理． 在文章的最后我们给出几个例子说明所获结论的正确性．

关键词: 正周期解, 时滞微分方程, 存在性, Schauder不动点定理

Abstract:

In this paper, we study the existence of positive periodic solutions for a particular class of first-order delay differential equations, where the linearized system may be degenerate. It is known that most methods may fail to guarantee the existence of periodic solution under the degenerate case. To alleviate this issue, this paper presents an efficient algorithm based on Schauder's fixed point theorem. Theorems which list the conditions for the existence of periodic solutions are presented. Simulation studies show the correctness of the improved method.

Key words: positive periodic solutions, delay differential equations, existence, Schauder's fixed point theorem

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