| 二阶离散Hamiltonian系统的多重变号周期解(英文) |
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| 引用本文： | 贺铁山,陈文革,雷友发. 二阶离散Hamiltonian系统的多重变号周期解(英文)[J]. 四川师范大学学报(自然科学版), 2010, 33(4). DOI: 10.3969/j.issn.1001-8395.2010.04.011 |
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| 作者姓名： | 贺铁山 陈文革 雷友发 |
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| 作者单位： | 1. 仲恺农业工程学院,计算科学系,广东,广州,510225
2. 华南理工大学,理学院,广东,广州,510640 |
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| 基金项目： | 广东省科技计划基金，福建省教育厅自然科学基金 |
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| 摘 要： | 研究了二阶非自治离散Hamilton系统多重变号周期解的存在性问题.在非线性项是奇函数的条件下,将这类Ham-ilton系统的变号周期解转化为定义在一个适当空间上泛函的临界点,然后利用Morse理论中的三临界点定理,建立了此类系统至少2个变号周期解的存在性结果,并举例说明了所获得的主要结果是有效的.
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| 关 键 词： | 变号周期解 离散Hamilton系统 临界点 |
Multiple Sign-changing Periodic Solutions of Second Order Discrete Hamiltonian Systems |
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| HE Tie-shan,CHEN Wen-ge,LEI You-fa. Multiple Sign-changing Periodic Solutions of Second Order Discrete Hamiltonian Systems[J]. Journal of Sichuan Normal University(Natural Science), 2010, 33(4). DOI: 10.3969/j.issn.1001-8395.2010.04.011 |
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| Authors: | HE Tie-shan CHEN Wen-ge LEI You-fa |
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| Abstract: | In this paper, we investigate the existence of multiple sign-changing periodic solutions for second order non-autonomous discrete Hamiltonian system. Under the condition that the nonlinearity is an odd function, we convert sign-changing periodic solutions of the system into the critical points of a functional defined on a proper space, and prove that there exist at least two different sign-changing periodic solutions. The approach used here is based on a 3 critical points theorem in the Morse theory. An illustrative example is given to demonstrate the effectiveness of the obtained main result. |
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| Keywords: | sign-changing periodic solution discrete Hamiltonian systems critical points |
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