一类具有时滞的Volterra微分系统周期解的存在唯一性  

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

作　　者：黄明辉 金楚华[2] HUANG Minghui;JIN Chuhua(Mathematics Teaching and Research Department,Guangzhou City Construction College,Guangzhou 510925;Faculty of Applied Mathematics,Guangdong University of Technology,Guangzhou 510090)

机构地区：[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

出　　处：《工程数学学报》2023年第3期471-482,共12页Chinese Journal of Engineering Mathematics

基　　金：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)。

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Krasnoselskii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。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.

关 键 词：Volterra微分系统 周期解 时滞 不动点 

分 类 号：O175.14[理学—数学]