| 具偏差变元的高阶泛函微分方程的周期解存在性问题 |
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| 引用本文： | 李晓静,鲁世平. 具偏差变元的高阶泛函微分方程的周期解存在性问题[J]. 系统科学与数学, 2009, 29(3): 367-377 |
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| 作者姓名： | 李晓静 鲁世平 |
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| 作者单位： | 1. 江苏技术师范大学数理学院,常州,213001;安徽师范大学数学系,芜湖,241000
2. 安徽师范大学数学系,芜湖,2410001 |
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| 基金项目： | 江苏技术师范学院基金，安徽省自然科学基金，安徽省教育厅自然科学基金重点项目 |
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| 摘 要： | 利用Fourier级数理论,伯努利数理论和重合度理论研究了一类具偏差变元的高阶泛函微分方程x(m)(t)+(m-1)∑(i=1)aix(i)(t)+f(x(t))+β(t)g(x(t-T(t)))=p(t)的周期解问题,得到了周期解存在的充分条件,有意义的是函数β(t)可变号.
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| 关 键 词： | 高阶泛函微分方程 重合度 周期解 |
| 收稿时间： | 2007-02-02 |
| 修稿时间： | 2007-06-26 |
The Existence of Periodic Solutions for a Kind of High-Order Functional Differential Equation |
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| LI Xiaojing,LU Shiping. The Existence of Periodic Solutions for a Kind of High-Order Functional Differential Equation[J]. Journal of Systems Science and Mathematical Sciences, 2009, 29(3): 367-377 |
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| Authors: | LI Xiaojing LU Shiping |
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| Affiliation: | (1) College of Mathematics and Physics, Jiangsu Teachers University of Technology, Changzhou} 213001;Department of Mathematics, Anhui Normal University, Wuhu Anhui 241000; (2)Department of Mathematics, Anhui Normal University, Wuhu Anhui 241000. |
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| Abstract: | In this paper, by using the theory of Fourier series, Bernoulli number theory andcontinuation theorem of coincidence degree theory, we study a kind of high-order functional differential equations with a deviating argument is considered. Some new results on the existence of periodic solutions are obtained. |
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| Keywords: | High-order functional differential equation coincidence degree periodic solution. |
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