| 一类二阶微分方程概周期解的存在性 |
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| 引用本文： | 祝文壮,冀书关,刘振华.一类二阶微分方程概周期解的存在性[J].吉林大学学报(理学版),2007,45(1):5-10. |
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| 作者姓名： | 祝文壮 冀书关 刘振华 |
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| 作者单位： | 1. 北京大学 数学学院, 北京 100871; 2. 吉林大学 数学学院, 长春 130012;3. 解放军艺术学院 舞蹈系, 北京 100081 |
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| 基金项目： | 吉林大学校科研和教改项目
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吉林大学校科研和教改项目 |
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| 摘 要： | 讨论一类二阶微分方程周期解和概周期解的存在性. 在g为连续同胚的假设下, 通过应用两次不动点定理证明了当e(t)为T周期函数时, 该方程存在惟一T周期解; 并利用逼近方法证明了当e(t)为概周期函数时, 该方程存在概周期解.
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| 关 键 词： | 二阶微分方程 周期解 概周期解 |
| 文章编号： | 1671-5489(2007)01-0005-06 |
| 收稿时间： | 2006-04-21 |
| 修稿时间： | 2006年4月21日 |
Existence of Almost Periodic Solution of a Class of Second Order Differential Equation |
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| ZHU Wen-zhuang,JI Shu-guan,LIU Zhen-hua.Existence of Almost Periodic Solution of a Class of Second Order Differential Equation[J].Journal of Jilin University: Sci Ed,2007,45(1):5-10. |
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| Authors: | ZHU Wen-zhuang JI Shu-guan LIU Zhen-hua |
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| Institution: | 1. School of Mathematics, Peking University, Beijing 100871, China; 2. College of Mathematics, Jilin University, Changchun 130012, China;3. Department of Dance, PLA Academy of Arts, Beijing 100081, China |
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| Abstract: | In this paper we discussed the existence of periodic and almost periodic solutions of a class of second order differential equation. Under the assumption that g is a continuous homeomorphism, we have proved using fixed point theorem twice that the equation has a uniqueTperiodic solution ife(t)is aT periodic function. Furthermore we have proved using approxi
mation method that the equation has almost periodic solution ife(t) is an a
lmost periodic function. |
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| Keywords: | second order differential equation periodic solution almost periodic solution |
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