| 一类高维变时滞微分系统周期解的存在性与唯一性 |
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| 引用本文： | 赵伟,武力兵. 一类高维变时滞微分系统周期解的存在性与唯一性[J]. 辽宁科技大学学报, 2013, 36(5): 495-500 |
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| 作者姓名： | 赵伟 武力兵 |
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| 作者单位： | 鞍山师范学院发展规划与质量监督处,辽宁鞍山,114016;辽宁科技大学理学院,辽宁鞍山,114051 |
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| 摘 要： | 在更为广泛的情况下,研究了一类高维变时滞微分系统x＇（t）=A（t,x（t））＋f（t,x（t-r1（t））,…,x（t-rm（t）））周期解的存在性与唯一性,分别利用Leray-Shauder不动点定理和压缩映照定理得到了其周期解存在与唯一的充分条件,所得结果推广和改进了已有文献中的相关结果.
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| 关 键 词： | 变时滞周期系统 泛函微分方程 周期解 |
Existence and uniqueness of periodic solutions for higher-dimensional variable time-delay differential system |
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| ZHAO Wei,WU Li bing. Existence and uniqueness of periodic solutions for higher-dimensional variable time-delay differential system[J]. Journal of University of Science and Technology Liaoning, 2013, 36(5): 495-500 |
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| Authors: | ZHAO Wei WU Li bing |
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| Affiliation: | 1. Department of Development Plannning and Quality Supervision, School of Science, College of Ansha.n Normal, Liaoning, Anshan 114016 China; 2. Department of Mathematics, School of Science, University of Science and Technology Liaoning, Anshan 114051 China) |
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| Abstract: | In the more extensively situation, the existence and uniqueness of periodic solutions for a class of higher-dimension variable time-delay differential systems is studied in the form of x＇（t）=A（t,x（t））＋f（t,x（t-r1（t））,…,x（t-rm（t）））The sufficient condition of the existence and uniqueness for periodic solutions is obtained by using Leray- Shauder fixed point theorem and compression mapping theorem, respectively, which improves and generaliz- es the corresponding results of the related literatures. |
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| Keywords: | variable time-delay periodic system functional differential equation periodic solutions |
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