| 时滞Duffing型方程周期解的存在唯一性 |
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| 引用本文： | 刘锡平,贾梅,任睿.时滞Duffing型方程周期解的存在唯一性[J].数学物理学报(A辑),2007,27(1):37-044. |
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| 作者姓名： | 刘锡平 贾梅 任睿 |
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| 作者单位： | 上海理工大学理学院，上海理工大学理学院，衡水学院数学系 上海 200093，上海 200093，衡水 053000 |
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| 摘 要： | 该文利用拓扑度方法研究了一类时滞依赖状态的广义Duffing型泛函微分方程x'(t)$ 该文利用拓扑度方法研究了一类时滞依赖状态的广义Duffing型泛函微分方程x'(t)$ 该文利用拓扑度方法研究了一类时滞依赖状态的广义Duffing型泛函微分方程x'(t) g(x(t-τ(t,x(t))))=f(t)周期解的存在性,得到了方程周期解存在的充分条件和必要条件．研究了当滞量为常值时,方程周期解的存在唯一性．并且给出了所研究问题的一个应用实例．
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| 关 键 词： | 时滞 Duffing型方程 周期解 度 |
| 文章编号： | 1003-3998(2007)01-037-08 |
| 收稿时间： | 2005-01-28 |
| 修稿时间： | 2005-01-28 |
On the Existence and Uniqueness of Periodic Solutions to a Type |
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| Liu Xiping,Jia Mei,Ren Rui.On the Existence and Uniqueness of Periodic Solutions to a Type[J].Acta Mathematica Scientia,2007,27(1):37-044. |
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| Authors: | Liu Xiping Jia Mei Ren Rui |
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| Institution: | College of Science, University of Shanghai for Science and Technology, Shanghai 200093;Department of Mathematics, Hengshui University, Hengshui 053000 |
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| Abstract: | By means of the methods presented in the topological degree theory, the existence of periodic solutions to a type of the DufRng functional differential equation x'(t) g(x(t-T(t,x(t))))=f(t) with complex time lag is studied, sufficient and necessary condition of the equation with periodic solutions is obtained, and the existence and uniqueness of periodic solutions is given when the time lag is constant, the instance is given to the problem. |
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| Keywords: | Time lag Duffing equation Periodic solutions Degree |
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