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具有两个偏差变元的Rayleigh方程的周期解的存在性 被引量：1

Periodic Solutions for the Rayleigh Equation with Deviating Arguments
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摘要 本文研究了一类具有两个偏差变元的Rayleigh方程的T-周期解的存在性问题。这是首次针对该类方程在其阻尼项满足Lipschitz条件的情况下进行的研究工作。通过一个改进的先验估计、运用一些分析技巧并利用迭合度的延拓定理,我们获得了方程存在周期解的新的结果。 In this paper, the existence of T-periodic solutions for a kind of Rayleigh equations with two deviating arguments is studied. This is the first time for investigating the equation in the case of the damping term satisfying the Lipschitz condition. A new result about the existence of periodic solutions is obtained by using an improved prior estimate, applying some analytic approaches and employing the continuation theorem of coincidence degree theory.
作者 周英告
机构地区 中南大学数学科学与计算技术学院
出处 《工程数学学报》 CSCD 北大核心 2008年第5期927-930,共4页 Chinese Journal of Engineering Mathematics
基金 国家自然科学基金(10471153) 中南大学博士后基金(第9批) 湖南省自然科学基金(06JJ2006)
关键词 延拓定理 RAYLEIGH方程 周期解 continuation theorem Rayleigh equation periodic solution
分类号 O175.14 [理学—基础数学]
  • 相关文献

参考文献7

  • 1Gains R E, Mawhin J L. Coincidence Degree and Nonlinear Differential Equations[M]. Lecture Notes in Mathematics, No. 568, Springer-Verlag, 1977.
  • 2Wang Gen-Qiang, Cheng Sui Sun. A priori bounds for periodic solutions of a delay Rayleigh equation[J]. Applied Mathematics Letters, 1999, 12:41-44.
  • 3Lu Shiping, Ge Weigao, Zheng Zuxiu. Periodic solutions for a kind of Rayleigh equation with a deviating argument[J]. Applied Mathematics Letters, 2004, 17:443-449.
  • 4鲁世平,葛渭高,郑祖庥.具偏差变元的Rayleigh方程周期解问题[J].数学学报（中文版）,2004,47(2):299-304. 被引量：35
  • 5Lu Shiping, Ge Weigao. Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument[J]. Nonlinear Analysis, 2004, 56:501-514.
  • 6Zhou Yinggao, Tang Xianhua. On existence of periodic solutions of Rayleigh equation of retarded type[J]. Journal Computational and Applied Mathematics, 2007, 203(1): 1-5.
  • 7Mawhin J, Willem M. Critical Point Theory and Hamittonian Systems[M]. New York: Springer-Verlag, 1989.

二级参考文献8

  • 1Gaines R. E., Mawhin J. L., Coincidence degree and nonlinear differential equations, Berlin: Springer-Verlag,1977.
  • 2Liu F., Existence of periodic solutions to a class of second order nonlinear differential equations, Acta Math.Sinica, 1990, 33(2): 260-269 (in Chinese).
  • 3Liu F., On the existence of periodic solutions of Rayleigh equation, Aeta Math. Sinica, 1994, 87(5): 639-644(in Chinese).
  • 4Huang X. K, Xiang Z. G., On the existence of 2π-periodic solution for delay Duffing equation x"(t)+g(x(t-τ))=p(t), Chinese Science Bulletin, 1994, 39(3): 201-203 (in Chinese).
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  • 6Lu S. P., Ge W. G., On the existence of periodic solutions of second order differential equations with deviating arguments, Acta. Math. Sinica, 2002, 45(4): 811-818 (in Chinese).
  • 7Lu S. P., Ge W. G., Periodic solutions for a kind of second order differential equations with multiple deviating arguments, Applied Mathematics and Computation, 2003, 146(1): 195-209.
  • 8Wang G. Q., A priori bounds for periodic solutions of a delay Rayleigh equation, Applied Mathematics Letters,1999, 12: 41-44.

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工程数学学报
2008年 第5期

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