| 引用本文： |
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刘永建,邓春红,冯春华.含n个滞量的微分差分方程周期解的存在性[J].广西科学,2005,12(4):259-261. [点击复制]
- Liu Yongjian,Deng Chunhong,Feng Chunhua.The Existence of Periodic Solutions of Differential Difference Equations with n Time Lags[J].Guangxi Sciences,2005,12(4):259-261. [点击复制]
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| 摘要: |
| 通过构造多元函数,定性分析一个耦合自治常微分方程组周期解的存在性,研究含多个滞量的微分差分方程x'(t)=F(x(t),x(t-f1),x(t-f2),…,x(t-fn))和x'(t)=F(x(t),x(t-f),x(t-2f),…,x(t-nf))周期解的存在性问题,获得系统存在非平凡振动周期解的一组充分条件,推广和改进了文献[3~5]的结果. |
| 关键词: 微分方程 微分差分方程 周期解 存在性 时滞 |
| DOI： |
| 投稿时间：2005-03-14修订日期：2005-04-19 |
| 基金项目:国家自然科学基金(10461003)资助项目。 |
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| The Existence of Periodic Solutions of Differential Difference Equations with n Time Lags |
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Liu Yongjian1, Deng Chunhong1,2, Feng Chunhua1
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| (1.College of Mathematics & Computer Science, Guangxi Normal University, Guilin, Guangxi, 541004, China;2.Department of Mathematics & Computer Science, Hunan University of Science & Technology, Yongzhou, Hunan, 425042, China) |
| Abstract: |
| By constructing multivariate function and qualitative analyzing the existence of periodic solutions of a coupled system of autonomous system of differential equations,the existence of non-constant oscillating periodic solutions of differential difference equations with n time lags x'(t)=F(x(t),x(t-f1),x(t-f2),…,x(t-fn))和x'(t)=F(x(t),x(t-f),x(t-2f),…,x(t-nf)) is studied.A set of sufficient conditions on the existence is obtained,the results of Reference[3~5] are extended and improved. |
| Key words: differential equation differential difference equation periodic solution existence time lags |
