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具偏差变元泛函微分方程周期解的存在定理 被引量：2

EXISTENCE THEOREM OF PERIODIC SOLUTION FOR FUNCTIONAL DIFFERENTIAL EQUATION WITH A DEVIATING ARGUMENT
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摘要 利用Mawhin重合度拓展定理研究了一类具偏差变元的泛函微分方程x(″t)+h(x(t))f(x(′t))+g(x(t-τ(t)))=p(t)的周期解问题,得到了周期解存在性的若干新结果,推广了已有的结果. By employing the continuation theorem of coincidence degree theory developed by Mawhin, a kind of functional differential equation with a deviating argument such as x″（t）＋h（x（t））f（x′（t））＋g（x（t-τ（t）））=p（t） is studied. Some new results on the existence of periodic solutions are obtained,which generalizes the known result（see [9] ）.
作者 陈新一
机构地区 西北民族大学中国民族信息技术研究院
出处 《北京工商大学学报（自然科学版）》 CAS 2010年第4期69-72,77,共5页 Journal of Beijing Technology and Business University:Natural Science Edition
关键词 周期解 偏差变元 重合度 periodic solution deviating argument coincidence degree
分类号 O175.6 [理学—基础数学]
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参考文献9

二级参考文献15

  • 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.
  • 10葛渭高，1985年

共引文献136

同被引文献18

  • 1黄先开,向子贵.具有时滞的Duffing型方程+g(x(t—τ))=p(t)的2π周期解[J].科学通报,1994,39(3):201-203. 被引量：90
  • 2刘峰.n维Rayleigh方程周期解的存在性[J].数学学报（中文版）,1994,37(5):639-644. 被引量：9
  • 3陈仕洲.具偏差变元高阶Lienard方程周期解存在性[J].纯粹数学与应用数学,2006,22(1):108-110. 被引量：12
  • 4Gaines R E, Mawhin J L. Coincidence degree and nonlinear differential equations[M].Berlin: Springer-Verlag, 1977.
  • 5Ma S. W, Wang Z. C, Yu J. S. Coincidence degree and periodic solutions of Duffing equations[J].Nonlinear Analysis, TMA, 1998,34:443-460.
  • 6Lu S. P, Ge W. G. Periodic solutions for a kind of second order differential equations with multiple deviating arguments[J]. Applied Mathematics and Computation, 2003, 146(1):195-209.
  • 7Wang G. Q, Cheng S. S. A priori bounds for periodic solutions of a delay Rayleigh equation[J].Applied Mathematics Letters, 1999,12:41-44.
  • 8LI J W,,WANG G Q.Sharp inequalities for periodic functions. Applied Math E-notes . 2005
  • 9Hale JK.Theory of functional differential equations. . 1977
  • 10Gaines RE,Mawhin JL.Coincidence degree and nonlinear differential equations. Lecture Notes in Mathematics . 1977

引证文献2

二级引证文献2

北京工商大学学报（自然科学版）
2010年 第4期

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