| 共振条件下2k阶微分方程的周期边值问题(英文) |
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| 引用本文： | 冯艳青,王忠英,陈荣军.共振条件下2k阶微分方程的周期边值问题(英文)[J].安徽大学学报(自然科学版),2011(1):10-14. |
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| 作者姓名： | 冯艳青 王忠英 陈荣军 |
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| 作者单位： | 常州工学院理学院; |
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| 基金项目： | Supported by the National Natural Science Foundation of China(20710015); the Natural Science Foundation of Jiangsu(YW06037); the Natural Science Foundation of Changzhou Institute of Technology(YN09090) |
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| 摘 要： | 2k阶微分方程周期解的存在和唯一性问题始终是学者们研究和探讨的一个重要课题。论文利用吸引盆理论和非负强制函数研究了Banach空间的全局同胚问题并应用于非线性方程,证明了2k阶微分方程周期解存在的充分条件,并证明相关文献中的结论是论文主要定理的推论.
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| 关 键 词： | 非负强制函数 吸引盆 全局同胚 周期解 共振 |
A resonance condition in the periodic boundary for 2kth order differential equations |
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| FENG Yan-qing,WANG Zhong-ying,CHEN Rong-jun.A resonance condition in the periodic boundary for 2kth order differential equations[J].Journal of Anhui University(Natural Sciences),2011(1):10-14. |
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| Authors: | FENG Yan-qing WANG Zhong-ying CHEN Rong-jun |
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| Institution: | FENG Yan-qing,WANG Zhong-ying,CHEN Rong-jun(College of Science,Changzhou Institute of Technology,Changzhou 213000,China) |
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| Abstract: | An important problem in the existence and uniqueness of 2 π-periodic solution for 2k th order differential equations with resonance had been extensively investigated by many authors.The basin of attraction and the nonnegative coercive function were the main tool of our explosion in discussing the global diffeomorphism between Banach spaces,a new set of sufficient conditions was obtained in studying the existence and uniqueness of 2kth order differential equations with resonance.The result of this paper generalized the other paper's conclusion and made it as a corollary. |
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| Keywords: | a nonnegative coercive function the basin of attraction homeomorphism periodic solution resonance |
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