利用Chapman-Kolmogorov等式和基本解矩阵、状态转移矩阵的概念，并结合Floquet理论，研究一类具有多变时滞的非线性中立型微分系统.首先，通过适当的积分变换得到系统解一个新的表达式.然后，利用Krasnoselskii不动点定理，给出了系统周期解的存在性，并在一定条件下构造适当的压缩映射得到该系统周期解的唯一性和零解稳定性的充分条件，改进了已有文献中的相应结果.
Abstract
By using the concepts of Chapman Kolmogorov equation, fundamental solution matrix and state transition matrix, and combining with Floquet theory, a class of nonlinear neutral differential system with delays are considered. Firstly, a new expression of the system solution is obtained by an appropriate integral transformation. Further, by using Krasnoselskii s fixed point theorem, the existence of periodic solutions for the system is given. Some sufficient conditions for the uniqueness of periodic solutions and stability of zero solutions are obtained by constructing an appropriate contractive mapping under certain conditions, which improve the corresponding results in the literature.
关键词
不动点定理 /
多变时滞 /
非线性微分系统 /
周期解 /
稳定性
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Key words
fixed point theorem /
variable delays /
nonlinear differential system /
periodic solutions /
stability
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参考文献
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脚注
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基金
国家自然科学基金（61773128）和2022年广州城建职业学院校级科研项目-自然科学项目（编号：2022ZKY10）成果资助.
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