| 一类时滞微分系统的周期解 |
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| 引用本文： | 刘可为.一类时滞微分系统的周期解[J].合肥学院学报(自然科学版),2008,18(2):7-10. |
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| 作者姓名： | 刘可为 |
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| 作者单位： | 合肥工业大学数学系,合肥,230009 |
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| 摘 要： | 研究了如下一类具分布与离散时滞的一阶微分系统x＇（t）=gradG（x（t）＋∫^0-rf（t,s,x（t＋s））ds＋g（t,x（t-θ（t））的周期解的存在性，其中G∈C^2（R^n,R）,f∈CR×-τ,0]×R^n,R^n）,g ∈ C（R×R^n,R^n）.利用重合度理论中的Mawhin延拓定理讨论了该时滞微分系统的周期解的存在性，建立了一些保证其周期解存在的充分性条件．
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| 关 键 词： | 时滞 微分系统 周期解 延拓定理 |
| 文章编号： | 1673-162X(2008)02-0007-04 |
| 修稿时间： | 2007年12月12 |
Periodic Solutions for a Class of Delay Differential Systems |
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| LIU Ke-wei.Periodic Solutions for a Class of Delay Differential Systems[J].Journal of Hefei University :Natural Sciences,2008,18(2):7-10. |
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| Authors: | LIU Ke-wei |
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| Institution: | LIU Ke-wei ( Department of Mathematics, Hefei University of Technology, Hefei 230009,China) |
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| Abstract: | In this paper, the existence of periodic solutions for the following a class of one order differential systems with distributed and discrete delaysx＇（t）=gradG（x（t）＋∫^0-rf（t,s,x（t＋s））ds＋g（t,x（t-θ（t））are presented, where there are G∈C^2（R^n,R）,f∈CR×-τ,0]×R^n,R^n）,g ∈ C（R×R^n,R^n）.By using Mawhin＇s continuation theorem of coincidence degree theory, the existence of periodic solutions for the delay differential systems is discussed. Some sufficient conditions to guarantee the existence of periodic solutions for the systems are established. |
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| Keywords: | delay differential systems periodic solutions continuation theorem |
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