| 二阶摆型振动方程奇调和解的存在性 |
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| 引用本文： | 陈太勇,张建军,刘文斌,张慧星.二阶摆型振动方程奇调和解的存在性[J].中国矿业大学学报,2004,33(4):491-494. |
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| 作者姓名： | 陈太勇 张建军 刘文斌 张慧星 |
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| 作者单位： | 中国矿业大学,理学院,江苏,徐州,221008 |
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| 摘 要： | 研究了二阶摆型振动方程奇调和解的存在性．运用Schwarz不等式估计方程解的先验界技巧和Leray—Schauder度理论得到了方程奇调和解的存在性定理，将Mawhin所给出的力函数周期性条件减弱为线性增长条件，从而改进了J Mawhin的结果．
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| 关 键 词： | 振动方程 奇调和解 Leray-Schauder度 函数 摆型振动 |
| 文章编号： | 1000-1964(2004)04-0491-04 |
| 修稿时间： | 2003年10月13 |
Existence of Odd-Harmonic Solutions for Second Order Pendulum-Type Oscillation Equations |
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| CHEN Tai-yong,ZHANG Jian-jun,LIU Wen-bin,ZHANG Hui-xing.Existence of Odd-Harmonic Solutions for Second Order Pendulum-Type Oscillation Equations[J].Journal of China University of Mining & Technology,2004,33(4):491-494. |
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| Authors: | CHEN Tai-yong ZHANG Jian-jun LIU Wen-bin ZHANG Hui-xing |
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| Abstract: | The existence of odd-harmonic solutions for a second order pendulum-type oscillation equation was studied. The existence theorems of solutions were obtained by using the technique of Schwarz's inequality to take prior estimate for solutions of the equation and the Leray-Schauder degree theory. In addition, the periodic condition for a force function given by Mawhin was weakened to the condition of linear growth. As a result, the some relative results given by J Mawhin were improved. |
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| Keywords: | pendulum-type oscillation equation odd-harmonic solution Leray-Schauder degree |
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