| 一类二阶微分方程概周期解的存在性 |
| |
| 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 |
| |
| 作者姓名： | 祝文壮 冀书关 刘振华 |
| |
| 作者单位： | 北京大学,数学学院,北京,100871;吉林大学,数学学院,长春,130012;吉林大学,数学学院,长春,130012;解放军艺术学院,舞蹈系,北京,100081 |
| |
| 基金项目： | 吉林大学校科研和教改项目 , 吉林大学校科研和教改项目 |
| |
| 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.
|
| 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： | 2006-04-21 |
Existence of Almost Periodic Solution of a Class of Second Order Differential Equation |
| |
| 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 |
| |
| Authors: | ZHU Wen-zhuang JI Shu-guan LIU Zhen-hua |
| |
| Affiliation: | 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 |
| |
| 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 approximation method that the equation has almost periodic solution ife(t) is an almost periodic function. |
| |
| Keywords: | second order differential equation periodic solution almost periodic solution |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
| 点击此处可从《吉林大学学报(理学版)》浏览原始摘要信息 |
|
点击此处可从《吉林大学学报(理学版)》下载全文 |
|
