| 二阶微分方程周期解的存在性和唯一性 |
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| 引用本文： | 魏元鸿,刘冬.二阶微分方程周期解的存在性和唯一性[J].吉林大学学报(理学版),2010,48(2):229-230. |
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| 作者姓名： | 魏元鸿 刘冬 |
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| 作者单位： | 1. 吉林大学 数学研究所, 长春 130012,2. 吉林大学 数学学院, 长春 130012 |
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| 基金项目： | 国家自然科学基金(批准号:J0630104) |
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| 摘 要： | 应用Schauder不动点定理研究二阶微分方程周期解的存在性和唯一性， 在右端函数连续可微时, 得到了周期解的存在性和唯一性, 并对右端函数仅为连续的情形给出了周期解存在的充分条件.
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| 关 键 词： | 周期解 Schauder不动点定理 存在性 唯一性 |
| 收稿时间： | 2010-02-24 |
Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations |
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| WEI Yuan-hong,LIU Dong.Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations[J].Journal of Jilin University: Sci Ed,2010,48(2):229-230. |
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| Authors: | WEI Yuan-hong LIU Dong |
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| Institution: | 1. Institute of Mathematics, Jilin University, Changchun 130012, China|2. College of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | The periodic solutions for second order differential equations were investigated by means of the Schauder's fixed point theorem. The existence and uniqueness of periodic solutions are established when the function f(t,x,x′) is continuously differentiable. Furthermore,under the condition that the right-hand function is only continuous,we have established the sufficient conditions for the existence of periodic solutions. |
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| Keywords: | periodic solutions Schauder's fixed point theorem existence uniqueness |
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