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基于一阶线性广义反射函数的非线性微分方程及其周期解 被引量：2

Based on first-order linear generalized reflection function of non-linear differential equation and periodic solution
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摘要 研究了具有一阶线性广义反射函数的微分方程的形式,研究了该类微分方程等价类,同时研究了该广义反射本身的形式.最后,研究了该微分方程的周期解与稳定性. This article studies, differential equation form of the first-order linear generalized reflection function, the equal kins of this kind of differential equation simultaneously and this generalized reflection＇s own form. It finally reveals this differential equation periodic solution and its stability.
作者 孙长军
机构地区 连云港职业技术学院数学教研室
出处 《华中师范大学学报（自然科学版）》 CAS CSCD 北大核心 2010年第2期207-209,共3页 Journal of Central China Normal University：Natural Sciences
基金 国家自然科学基金项目(60774073) 江苏省教委自然科学研究基金(BK2007075)
关键词 一阶线性 广义反射函数 微分方程 周期解 稳定性 first-order linear generalized reflection function differential equation periodic solution stability
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献10

  • 1Mironenko V I. On the method that allows one to determine the initial data of periodic solution of differential systems and to compare the mappings for a period [J]. Differential Equations, 1980,14(11) : 1985-1994.
  • 2Mironenko V I. Reflecting Function and Periodic Solution of the Differential Equations[M]. Minsk:University Press, 1986.
  • 3Alisevich L A. On linear system with triangular reflective function [J].Differ Eq,1983,19(8) :1446-1449.
  • 4Veresovich P P. Nonautonomous second order quadratic sys tern equivalent to linear system [J]. Differ Eq,1998,14(12):2257-2259.
  • 5Mironenko V V. Time symmetry preserving perturbations of differential systems[J].Differential Equations, 2004, 40 (10) : 1395-1403.
  • 6Musafirov E V. Differential systems,the mapping over period for which is represented by a product of three exponential matrixes[J]. Journal of Mathematical Analysis and Applications,2007,229(1) :647-654.
  • 7Zhou Zhengxin. Nonlinear reflective function and periodic solution of differential systems[J]. Applied Math Letter, 2004, 7(10) :1121-1125.
  • 8Zhou Zhengxin. The nonlinear reflective function of differential system[J].Nonlinear Analysis,2003, 53:733 -741.
  • 9Zhou Zhengxin. On the Poincare mapping and Periodic Solutions of nonautonomous differential systems[J]. Communica tions on Pure and Applied Analysis, 2007,60(2):541-547.
  • 10周正新.微分系统的反射函数与周期解[J].数学进展,2003,32(4):398-404. 被引量：21

二级参考文献5

共引文献20

同被引文献18

  • 1Mironenko V I.On the method that allows one to determine the initial data of periodic solution of differential systems and to compare the mappings for a period[J].Differential Equations,1980,14 (11):1985-1994.
  • 2Mironenko V I.Reflecting function and periodic solution of the differential equations[M].Minsk:University Press,1986:12-26.
  • 3Alisevich L A.On linear system with triangular reflective function[J].Differ.Eq.,1983,19(8):1446-1449.
  • 4Veresovich P P.Nonautonomous second order quadratic system equivalent to linear system[J].Differ.Eq.,1998,14(12):2257-2259.
  • 5Musafirov E V.Differential systems,the mapping over period for which is represented by a product of three exponential matrixes[J].Journal of Mathematical Analysis and Applications,2007,229(1):647-654.
  • 6Zhou Zhengxin.On the Poincaré mapping and periodic solutions of nonautonomous differential systems[J].Communications on Pure and Applied Analysis,2007,60(2):541-547.
  • 7Mironenko V I. On the method that allows one to determine the initial data of periodic solution of differential systems and to compare the mappings for a period[J].Differential Equations,1980,14(ll):1985- 1994.
  • 8Mironenko V I. Reflecting function and periodic solution of the differential equations[M]. Minsk:University Press, 1986:12-26.
  • 9Alisevich L A .On linear system with triangular reflective function[J]. Differ.Eq.,1983,19(8):1446-1449.
  • 10Veresovich P P. Nonautonomous second order quadratic system equivalent to linear system [J]. Differ.Eq.,1998,14(12):2257-2259.

引证文献2

二级引证文献4

华中师范大学学报（自然科学版）
2010年 第2期

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