[1]孟青,张福保.含有次凸位势的二阶Hamilton系统周期解[J].东南大学学报(自然科学版),2009,39(1):181-184.[doi:10.3969/j.issn.1001-0505.2009.01.035]
 Meng Qing,Zhang Fubao.Periodic solutions of the second order Hamiltonian systems with subconvex potentials[J].Journal of Southeast University (Natural Science Edition),2009,39(1):181-184.[doi:10.3969/j.issn.1001-0505.2009.01.035]
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含有次凸位势的二阶Hamilton系统周期解()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
39
期数:
2009年第1期
页码:
181-184
栏目:
数学、物理学、力学
出版日期:
2009-01-20

文章信息/Info

Title:
Periodic solutions of the second order Hamiltonian systems with subconvex potentials
作者:
孟青 张福保
东南大学数学系, 南京 210096
Author(s):
Meng Qing Zhang Fubao
Department of Mathematics, Southeast University, Nanjing 210096,China
关键词:
周期解 非自治Hamilton系统 极小作用原理 鞍点定理
Keywords:
periodic solutions non-autonomous Hamiltonian systems the least action principle saddle point theorem
分类号:
O175
DOI:
10.3969/j.issn.1001-0505.2009.01.035
摘要:
研究非自治的二阶Hamilton系统:±(¨overu)=F(t,u(t)),a.e.t∈[0,T],u(0)-u(T)=(·overu)(0)-(·overu)(T)=0的周期解. 当位势函数是一个(λ,μ)次凸函数与一个次二次函数的和时, 利用极小作用原理和鞍点定理得到了非平凡周期解存在的几个充分条件. 更全面地讨论了含有(λ,μ)次凸位势的Hamilton系统的周期解, 推广和补充了某些已知的结果.
Abstract:
The non-autonomous second order Hamiltonian systems:±(¨overu)=F(t,u(t)),a.e.t∈[0,T],u(0)-u(T)=(·overu)(0)-(·overu)(T)=0 have been studied. The problems with potentials being the sums of(λ,μ)subconvex functions and subquadratic functions are considered by the least action principle and the saddle point theorem. Some sufficient conditions for nontrivial periodic solutions are obtained. Periodic solutions of Hamiltonian systems with(λ,μ)subconvex potentials are discussed comprehensively. The results provide a generalization and complement for some known ones.

参考文献/References:

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备注/Memo

备注/Memo:
作者简介: 孟青(1983—),女,硕士生; 张福保(联系人),男,教授,zhangfubao@seu.edu.cn.
引文格式: 孟青,张福保.含有次凸位势的二阶Hamilton系统周期解[J].东南大学学报:自然科学版,2009,39(1):181-184.
更新日期/Last Update: 2009-01-20