| 扰动Van der Pol方程的周期解（英文） |
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| 引用本文： | 任秀芳.扰动Van der Pol方程的周期解（英文）[J].南京大学学报(自然科学版),2014(2):125-139. |
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| 作者姓名： | 任秀芳 |
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| 作者单位： | 南京农业大学理学院数学系 |
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| 基金项目： | Supported by NSFC(No.11126100);the Youth Science and Technology Innovation Fund of Nanjing Agricultural University(No.KJ2010025);the Jiangsu Overseas Research&Tranning Program for University Prominent Young&Middle-aged Teachers and Presidends |
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| 摘 要： | 本文证明了带小参数扰动的Van der Pol方程周期解的存在性和稳定性.主要通过构造周期函数空间上的若干算子,应用巴拿赫空间上的压缩映像原理,对线性变分方程的特征指数做分析得到结论.
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| 关 键 词： | Van der Pol方程 周期解 存在性 稳定性 |
PERIODIC SOLUTIONS OF PERTURBED VAN DER POL EQUATION |
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| Ren Xiufang.PERIODIC SOLUTIONS OF PERTURBED VAN DER POL EQUATION[J].Journal of Nanjing University: Nat Sci Ed,2014(2):125-139. |
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| Authors: | Ren Xiufang |
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| Institution: | Ren Xiufang;Department of Mathematics,Nanjing Agricultural University; |
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| Abstract: | In this paper,we show the existence and stability of the periodic solutions of van der Pol equation with a small perturbation.The proof is based on constructing several operators in the periodic function space,applying Banach contracting-mapping principle and analyzing the characteristic exponent of the related variational equation. |
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| Keywords: | van der Pol equation periodic solution existence stability |
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