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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 ›› 2023, Vol. 40 ›› Issue (3): 471-482.doi: 10.3969/j.issn.1005-3085.2023.03.010

• • 上一篇    下一篇

一类具有时滞的Volterra微分系统周期解的存在唯一性

黄明辉1,  金楚华2   

  1. 1. 广州城建职业学院数学教研室，广州 510925 
    2. 广东工业大学应用数学学院，广州 510090
  • 收稿日期:2020-08-22 接受日期:2023-02-14 出版日期:2023-06-15 发布日期:2023-08-15
  • 基金资助:
    国家自然科学基金 (61773128)；广东省普通高校青年创新人才项目(自然科学) (2022KQNCX289)；2022年广州城建职业学院课题 (JGXZYB202243).

Existence and Uniqueness of Periodic Solution to a Class of Volterra Differential System with Delays

HUANG Minghui1,  JIN Chuhua2   

  1. 1. Mathematics Teaching and Research Department, Guangzhou City Construction College, Guangzhou 510925 
    2. Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510090
  • Received:2020-08-22 Accepted:2023-02-14 Online:2023-06-15 Published:2023-08-15
  • Supported by:
    The National Natural Science Foundation of China (61773128); the Guangdong Provincial University Youth Innovation Talent Project (Natural Science) (2022KQNCX289); 2022 Guangzhou City Construction College Project (JGXZYB202243).

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摘要：

探讨了一类具有时滞的Volterra微分系统的周期解问题。利用基本解矩阵、Floquet理论等工具，对Volterra系统进行积分变换，构造其系统解新的表达式；利用Krasno-selskii不动点方法，获得了所研究系统周期解的存在性；利用压缩映射原理获得了系统周期解唯一性的充分性条件。最后，通过实例验证了结论的有效性。

关键词: Volterra微分系统, 周期解, 时滞, 不动点

Abstract:

The periodic solutions for a class of Volterra differential systems with delays are discussed. By using techniques such as the fundamental solution matrix and Floquet theory, the Volterra system is integrally transformed to construct a new expression for the system solution; By using the Krasnoselskii fixed point method, the existence of periodic solutions for the studied system is obtained; the sufficient conditions for the uniqueness of the periodic solution of the system are obtained by using the contraction mapping principle. Finally, an example is given to verify the effectiveness of the conclusion.

Key words: Volterra differential system, periodic solution, delays, fixed point

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