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一类非线性摆方程的伪概周期解 被引量：2

The Pseudo Almost Periodic Solution of the Nonlinear Pendulum Equations
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摘要 利用伪概周期函数的性质和Banach压缩映像原理研究了一类常见非线性摆方程的伪概周期解问题,证明了该伪概周期解的存在性及在‖u‖L∞<1中的唯一性。 In this paper,the Nonlinear Pendulum equation is studied.The pseudo almost periodic solution is found,and its uniqueness in ‖u‖L∞1 is also got.The crucial tools in the proofs are pseudo almost periodic functions and Banach contraction mapping principle.
作者 邱汶华
机构地区 枣庄学院
出处 《廊坊师范学院学报（自然科学版）》 2010年第3期15-16,共2页 Journal of Langfang Normal University(Natural Science Edition)
基金 枣庄学院青年项目(2009QN43)
关键词 摆方程 伪概周期解 Banach压缩映像原理 pendulum equation pseudo almost periodic solution banach contraction mapping principle
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献5

  • 1Guckenheimer J, Holmes P. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields [ M ]. New York: Springer Verlag, 1983.
  • 2Andres Jan. Existence of the two almost periodic solutions of the forced pendulum Equation [ J ]. Nonlinear Analysis, 1999, 37:797 - 804.
  • 3朴大雄,辛娜.受迫摆方程的伪概周期解[J].中国海洋大学学报（自然科学版）,2007,37(4):573-575. 被引量：6
  • 4邱汶华.一类广义摆方程的伪概周期解[J].佳木斯大学学报（自然科学版）,2009,27(2):298-300. 被引量：2
  • 5Zhang C. Pseudo almost periodic functions and their applications, Thesis[ M ]. USA: the University of Western Ontario, 1992.

二级参考文献11

  • 1Guckenheimer J, Holmes P , Nonlinear Oscillations. Dynamical Systems and Bifurcations of Vector Fields[ M]. New York:Springer Verlag,198B.
  • 2Andres Jan. Existence of the Two Almost Periodic Solutions of the Forced Pendulum Equation[J]. Nonlinear Analysis, 1999, 37:797 -804.
  • 3Zhang C. Pseudo Almost Periodic Functions and Their Applications, Thesis[M]. USA: the University of Western Ontario, 1992,
  • 4A.M.Fink. Almost Periodic Differential Equations, Lecture Notes in Mathematics[M]. Vol.377, Springer-Verlag, Berlin, 1974.
  • 5朴大雄,辛娜.受迫摆方程的伪概周期解[J].中国海洋大学学报（自然科学版）,2007,37(4):573-575. 被引量：6
  • 6Guckenheimer J,Holmes P,Nonlinear Oscillations.Dynamical Systems and Bifurcations of Vector Fields[M].New York:SpringerVerlag,1983.
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  • 9Zhang C.Pseudo almost periodic solutions of some differential equations Ⅱ[J].J.Math.Anal.Appl,1995,192:543-561.
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共引文献5

同被引文献14

  • 1朴大雄,邱汶华.一类广义Sine-Gordon方程的概周期解[J].中国海洋大学学报（自然科学版）,2006,36(6):892-894. 被引量：4
  • 2李永祥.电报方程双周期解的极大值原理与强正性估计及应用[J].数学学报（中文版）,2007,50(4):895-908. 被引量：3
  • 3朴大雄,辛娜.受迫摆方程的伪概周期解[J].中国海洋大学学报（自然科学版）,2007,37(4):573-575. 被引量：6
  • 4Ortega R,Robles-Perez A M. A maximum principle for periodic solutions of the telegraph equation[J]. J. Math. Anal. Appl. ,1998,221:625 -651.
  • 5Mawhin J, Ortega R, Robles-Perez A M. A maximum principle for bounded solutions of the telegraph equations and applications to nonlinear forcings[J].J.Math.Anal.Appl.,2000,251:695-709.
  • 6Mawhin J,Ortega R,Robles-Perez A M.Maximum principle for bounded solutions of the telegraph equation in space dimensions two and three and applications [J]. J. Differential Equations,2005,208:42-63.
  • 7Guckenheimer J, Holmes P. Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Field[M]. New York: Springer-Verlag, 1983.
  • 8Andres Jan. Existence of the two almost periodic so- lutions of the forced pendulum Equation[J]. Nonlinear Anal- ysis, 1999,37 : 797-804.
  • 9Fink A M. Almost periodic differential equations[J]. Lecture Notes on Mathematics, 1974,337: 80-112.
  • 10Zhang C Y. Pseudo almost periodic solutions to a class of semilinear differential equations[J]. J.Math.Anal.Ap- pl, 1994,181(1):62-76.

引证文献2

廊坊师范学院学报（自然科学版）
2010年 第3期

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