| 多项式微分方程的广义反射函数及其周期解 |
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| 引用本文： | 潘颖昕,高巧萍,刘文俊.多项式微分方程的广义反射函数及其周期解[J].淮海工学院学报,2014(2):11-13. |
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| 作者姓名： | 潘颖昕 高巧萍 刘文俊 |
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| 作者单位： | [1]如皋高等师范学校数理与信息技术系,江苏如皋226500 [2]扬州大学数学科学学院,江苏扬州225002 |
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| 基金项目： | 江苏省高等学校大学生实践创新训练计划资助项目（201311117084X） |
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| 摘 要： | 为了研究多项式微分方程周期解的存在性与稳定性,通过多项式微分方程的广义反射函数来寻找其Poincaré映射.给出了多项式微分方程具有线性广义反射函数的充要条件,以及在该条件下线性广义反射函数的具体表达式和多项式微分方程周期解的存在性与稳定性.该结果对研究相关微分方程周期解与稳定性具有一定的参考价值和指导意义.
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| 关 键 词： | 多项式微分方程 广义反射函数 周期解 |
Generalized Reflective Function and Periodic Solution of Polynomial Differential Equation |
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| PAN Ying-xin,GAO Qiao-ping,LIU Wen-jun.Generalized Reflective Function and Periodic Solution of Polynomial Differential Equation[J].Journal of Huaihai Institute of Technology:Natural Sciences Edition,2014(2):11-13. |
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| Authors: | PAN Ying-xin GAO Qiao-ping LIU Wen-jun |
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| Affiliation: | 1. Dept. of Mathematics, Physics and Information Technology, Rugao Higher Normal School, Rugao 226500, China; 2. School of Mathematics, Yangzhou University, Yangzhou 225002, China) |
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| Abstract: | In order to study the problem associated with periodic solution and stability of polyno-mial differential equation,this paper proposes a method to find its Poincare mapping through polynomial differential equation’s generalized reflective function.It establishes the necessary and sufficient conditions for polynoe genermial differential equation to have linear generalized reflective function.Under these conditions the form of thalized reflective function has been established and the existence and stability of the periodic solution has been discussed.This study is of reference and guiding value for researches on the periodic solution and the stability of other differential equations. |
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| Keywords: | polynomial differential equation generalized reflective function periodic solution |
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