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一类具偏差变元的二阶微分方程周期解 被引量：9

Periodic Solutions for a Kind of Second Order Differential Equation with a Deviating Argument
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摘要 利用M ahw in重合度拓展定理研究了一类具偏差变元的二阶微分方程x″(t)+f(x′(t))+h(x(t))x′(t)+g(x(t-τ(t)))=p(t)周期解问题,得到了周期解存在的一组充分条件. Employing the continuation theorem of coincidence degree theory developed by Mawhin, we study a kind of second order differential equation with a deviating argument as follows x^n（t）＋f（x＇（t））＋h（x（t））x＇（t）＋g（x（t-r（t）））=p（t） we get some sufficient conditions of existence of periodic solution.
作者 杜波 鲁世平
机构地区 安徽师范大学数学计算机科学学院
出处 《数学研究》 CSCD 2007年第1期16-21,共6页 Journal of Mathematical Study
基金 安徽省教育厅自然科学基金重点项目(2005kj031ZD) 安徽省自然科学基金项目(050460103)
关键词 周期解 重合度 偏差变元 periodic solutions coincidence degree deviating argument
分类号 O175.14 [理学—基础数学]
  • 相关文献

参考文献8

  • 1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
  • 2Wang G Q. A priori bounds for periodic solutions of a delay Rayleigh equation,Applied Mathematics Letters, 1999,12:41--44.
  • 3Iannacci R, Nkashama M N. On periodic solutions of forced second order differential equations with a deviating argument. Lecture Notes InMath. , 151 ,Springer-Verlag, 1984,224-- 232.
  • 4Li Yongkun. Periodic solutions of Lienard equations with deviating arguments ,J. Math Research and Exposition, 1998,18:565--570.
  • 5鲁世平,葛渭高.一类二阶具偏差变元的微分方程周期解[J].数学学报（中文版）,2002,45(4):811-818. 被引量：40
  • 6Lu Shiping, Ge Weigao. Periodic solutions for a kind of Lienard equations with deviating arguments. J.Math. Anal. Appl. , 2004, 249:231--243.
  • 7Lu Shiping, Ge Weigao. Some new results on the existence of periodic solutions to a kind of Rayleigh equation with deviating arguments. Nonlinear Analysis, 2004, 56 : 501-- 514.
  • 8Gaines R, Mawhin J. Coincide Degree and Nonlinear Differential Equation. Berlin:Springer-Verlag,1977.

二级参考文献9

  • 1黄先开.具有时滞的保守系统的2π周期解[J].系统科学与数学,1989,9(4):298-308. 被引量：17
  • 2Gaines R. E., Mawhin J. L., Coincidence degree and nonlinear differential equations, Berlin: Springer-Verlag,1977.
  • 3Liu F., Existence of periodic solutions to a class of second order nonlinear differential equations, Acta Math.Sinica, 1990, 33(2): 260-269 (in Chinese).
  • 4Liu F., On the existence of periodic solutions of Rayleigh equation, Aeta Math. Sinica, 1994, 87(5): 639-644(in Chinese).
  • 5Huang 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).
  • 6Ma S. W., Wang Z. C., Yu J. S., Coincidence degree and periodic solutions of Dufling equations, Nonlinear Analysis, TMA, 1998, 84: 443-460.
  • 7Lu 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).
  • 8Lu 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.
  • 9Wang G. Q., A priori bounds for periodic solutions of a delay Rayleigh equation, Applied Mathematics Letters,1999, 12: 41-44.

共引文献64

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引证文献9

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数学研究
2007年 第1期

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