The Existence of Periodic Solutions of Delay Differential Equations by E + -Conley Index Theory
The Existence of Periodic Solutions of Delay Differential Equations by E + -Conley Index Theory
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基于E-Conley指数理论时滞微分方程周期解的存在性
DOI：
10.1155/2022/3396716
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Huafeng Xiao
中科院分区：
文献类型：
--
作者：
Huafeng Xiao
本文利用E + -Conley指标理论研究了一类非自治时滞微分方程周期解的存在性。建立了微分方程的变分结构，将微分方程周期解的存在性转化为相应函数临界点的存在性。当微分方程为2 π -非共振时，得到了周期解存在的充分条件.当系统在无穷远点2 π共振时，利用原泛函的二次扰动，得到了系统周期解存在的充分条件.
In this paper, the E + -Conley index theory has been used to study the existence of periodic solutions of nonautonomous delay differential equations (in short, DDEs). The variational structure for DDEs is built, and the existence of periodic solutions of DDEs is transferred to that of critical points of the associated function. When DDEs are 2 π -nonresonant, some sufficient conditions are obtained to guarantee the existence of periodic solutions. When the system is 2 π -resonant at infinity, by making use a second disturbing of the original functional, some sufficient conditions are obtained to guarantee the existence of periodic solutions to DDEs.