| 一类非线性Duffing方程概周期解的存在性 |
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| 引用本文： | 张留伟,徐远通.一类非线性Duffing方程概周期解的存在性[J].中山大学学报(自然科学版),2010,49(4). |
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| 作者姓名： | 张留伟 徐远通 |
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| 作者单位： | 中山大学数学与计算科学学院,广东,广州,510275 |
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| 摘 要： | 研究了一类广义非线性Duffing方程概周期解的存在性。通过Lyapunov函数建立辅助线性方程的指数型二分性,在此基础上,选取适当的函数空间,利用不动点定理,得到广义非线性Duffing有界解的存在性,再次利用Lyapunov函数,得到其概周期解的存在性和模包含关系。
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| 关 键 词： | Duffing方程 概周期 指数型二分性 Lyapunov函数 |
| 收稿时间： | 2009-06-09; |
Existence of Almost Periodic Solutions for Some Nonlinear Duffing Equations |
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| ZHANG Liuwei,XU Yuantong.Existence of Almost Periodic Solutions for Some Nonlinear Duffing Equations[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2010,49(4). |
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| Authors: | ZHANG Liuwei XU Yuantong |
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| Institution: | (School of Mathematics and Computational Science, Sun Yat sen University, Guangzhou 510275, China) |
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| Abstract: | The existence of almost periodic solutions of some more generalized nonlinear Duffing equations is studied. Firstly, by means of the Lyapunov functions, the exponential dichotomy of the auxiliary linear equations is established. Then, by combining the fixed point theorem in some suitable space, using the Lyapunov function again, the existence of almost periodic solutions of the nonlinear Duffing equations and module inclusion are obtained. |
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| Keywords: | Duffing equations almost periodicity exponential dichotomy Lyapunov functions |
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