| 二阶微分方程求解周期解的变分方法 |
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| 引用本文： | 贾秀利,王振华,关丽红.二阶微分方程求解周期解的变分方法[J].吉林大学学报(理学版),2013,51(2):164-168. |
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| 作者姓名： | 贾秀利 王振华 关丽红 |
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| 作者单位： | 1. 吉林工商学院 基础部, 长春 130062,2. 吉林大学 数学研究所, 长春 130012;3. 长春大学 理学院, 长春 130022 |
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| 基金项目： | 国家自然科学基金(批准号:11171130);吉林省教育厅“十一五”规划社会科学研究项目(批准号:吉教科文合字[2010]第521号) |
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| 摘 要： | 利用等价变分方法研究一类二阶微分方程的周期解问题. 通过寻找适当变换, 将原来的二阶周期边值问题约化为易于求解的一阶周期边值问题, 进而求得周期解. 应用实例验证了该方法的有效性.
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| 关 键 词： | 微分方程 周期解 等价变分 |
| 收稿时间： | 2012-09-07 |
Periodic Solutions of Second Order Differential Equations |
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| JIA Xiu-li,WANG Zhen-hua,GUAN Li-hong.Periodic Solutions of Second Order Differential Equations[J].Journal of Jilin University: Sci Ed,2013,51(2):164-168. |
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| Authors: | JIA Xiu-li WANG Zhen-hua GUAN Li-hong |
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| Institution: | 1. Department of Basic Course, Jilin Business and Technology College, Changchun 130062, China;2. Institute of Mathematics, Jilin University, Changchun 130012, China;3. College of Science, Changchun University, Changchun 130022, China |
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| Abstract: | The periodic solutions of a class of second order differential equations were studied with the equivalent variational method. By finding suitable transformation, the original second order periodic boundary value problem was reduced to the first order periodic boundary value problem in which the periodic solution is more easily obtained. Finally, the application to a class of examples was given to illustrate the potential of this method. |
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| Keywords: | differential equation periodic solution equivalent variation |
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