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| Periodic Solutions of Nonautonomous Second Order Hamiltonian Systems | |
| 引用本文： | Shi Xia LUAN An Min MAO. Periodic Solutions of Nonautonomous Second Order Hamiltonian Systems[J]. 数学学报(英文版), 2005, 21(4): 685-690. DOI: 10.1007/s10114-005-0532-6 |
| 作者姓名： | Shi Xia LUAN An Min MAO |
| 作者单位： | [1]Department of Mathematics, Qufu Normal University, Qufu 273165. P. R. China [2]Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. Beijing 100080. P. R. China |
| 摘 要： | In this paper, we develop the local linking theorem given by Li and Willein by replacing the Palais-Smale condition with a Cerami one, and apply it to the study of the existence of periodic solutions of the nonautonomous second order Hamiltonian systems （H） ü＋A（t）u＋∨V（t, u）=0, u∈R^N, t∈R. We handle the case of superquadratic nonlinearities which differ from those used previously. Our results extend the theorems given by Li and Willem. |
| 关 键 词： | 非自控系统 Hamiltonian函数 周期解 局部连接 临界点 |
| 收稿时间： | 2004-12-21 |
Periodic Solutions of Nonautonomous SecondOrder Hamiltonian Systems |
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| Shi Xia Luan,An Min Mao. Periodic Solutions of Nonautonomous SecondOrder Hamiltonian Systems[J]. Acta Mathematica Sinica(English Series), 2005, 21(4): 685-690. DOI: 10.1007/s10114-005-0532-6 | |
| Authors: | Shi Xia Luan An Min Mao |
| Affiliation: | (1) Department of Mathematics, Qufu Normal University, Qufu 273165, P. R. China;(2) Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, P. R. China |
| Abstract: | In this paper, we develop the local linking theorem given by Li and Willem by replacing the Palais–Smale condition with a Cerami one, and apply it to the study of the existence of periodic solutions of the nonautonomous second order Hamiltonian systems ℋ ü + A(t) u + ∇V (t, u) = 0, u ∈ ℝ N, t ∈ ℝ. We handle the case of superquadratic nonlinearities which differ from those used previously. Our results extend the theorems given by Li and Willem. Supported by NSFC (10471075) and NSFSP (Y2003A01) and NSFQN (xj0503) |
| Keywords: | Non-autonomous Hamiltonian systems Periodic solutions Local linking Critical point theory Variational method |
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