| 引用本文: | 刘易成,李志祥.高维无穷时滞NFDE概周期解的存在性和稳定性.[J].国防科技大学学报,2003,25(6):67-71.[点击复制] |
| LIU Yicheng,LI Zhixiang.The Existence and Stability of the Almost Periodic Solutions of the Higher Dimensional NFDE with Infinite Delay[J].Journal of National University of Defense Technology,2003,25(6):67-71[点击复制] |
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| 高维无穷时滞NFDE概周期解的存在性和稳定性 |
| 刘易成, 李志祥 |
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(国防科技大学 理学院，湖南 长沙 410073)
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| 摘要: |
| 讨论高维的中立型泛函微分方程 d/d t[x(t)-∫0-∞q(s)x(t+s)ds］=A(t,x)x(t)+f(t,xt) 的概周期解问题。利用 Ch 空间,矩阵测度和Krasnoselski不动点定理获得了其概周期解的存在性与惟一性定理。特别地,当q=0时给出了存在惟一且一致稳定概周期解的条件,推广了文献［1～5］的结果。 |
| 关键词: 中立型泛函微分方程 概周期解 矩阵测度 稳定性 |
| DOI： |
| 投稿日期：2003-04-04 |
| 基金项目:校预研基金资助项目 |
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| The Existence and Stability of the Almost Periodic Solutions of the Higher Dimensional NFDE with Infinite Delay |
| LIU Yicheng, LI Zhixiang |
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(College of Science, National Univ. of Defense Technology,Changsha 410073, China)
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| Abstract: |
| The authors investigate the almost periodic solution of neutral functional equation with infinite delay of the following d/dt[x(t)-∫0-∞q(s)x(t+s)ds］=A(t,x)x(t)+f(t,xt) Some results on the existence and uniqueness of almost periodic solutions are obtained by use of Ch space, matrix measure and Krasnoselskii's fixed theorem. Especially, whenq(s)is zero matrix, we derive sufficient conditions for the existence of a unique and uniformly stable almost periodic solution, which generalizes several results in references［1～5］. |
| Keywords: neutral functional differential equation almost periodic solution matrix measure stability |
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