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一类二阶自共轭矩阵微分系统的区间振动定理 被引量：1

Oscillation Theorems for Certain Second Order Self-Adjoint Matrix Differential Systems on Interval
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摘要 本文运用单调泛函和广义区间平均方法,获得了一类二阶自共轭矩阵微分系统[P(t)X'(t)]'+Q(t)X(t)=0的一些新的区间振动定理. By means of monotone functionals and the generalized interval means method, some new oscillation criteria for self-adjoint differential matrix system of the form [P（t）X＇（t）]＇ ＋ Q（t）X（t） = 0 are obtained.
作者 杨启贵
机构地区 华南理工大学数学科学学院
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2005年第5期1011-1020,共10页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金资助项目(10461002)广西省自然科学基金资助项目(0236012)
关键词 矩阵微分系统 单调泛函 振动定理 Matrix differential system Monotone functional Oscillation criterion
分类号 O174.2 [理学—基础数学]
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参考文献22

  • 1Butler G. J., Erbe L. H., Mingarelli A. B., Riccati techniques and variational principle in oscillatory theory for linear system, Trans. Amer. Math. Soc., 1987, 303: 263-282.
  • 2Byers R., Harris B. J., Kwong M. K., Weighted means and oscillation of second order matrix differential system, J. Diff. Eqs., 1986, 61: 164-177.
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同被引文献20

  • 1Leighton W.On self-adjoint differential equations of second order.J.London Math.Soc,1952, 27:37-47.
  • 2Wintner A.A criteria of oscillatory stability.Quart.Appl.Math.,1949,7:115-117.
  • 3Hartman P.On nonoscillatory linear differential equation of second order.Amer.J.Math.,1952, 74:389-400.
  • 4Coles W J.An oscillation for linear second order differential equations.Proc.Amer.Math.Soc, 1968,19:755-759.
  • 5Macki J W,Wong J S W.Oscillation theorems for linear second order differential equations.Proc. Amer.Math.Soc,1969,20:67-72.
  • 6Etgen G J,Pawlowski J F.Oscillation criteria for second order self adjoint matrix differential systems.Pacific J.Math.,1976,66:99-110.
  • 7Parhi N,Praharaj P.Oscillation criteria for second order self-adjoint matrix differential equations. Annal.Polonici Math.,1999,LXXⅡ:1-14.
  • 8Kumari I S,Umamaheswaram S.Oscillation criteria for linear matrix Hamiltonian system.J. Differential Eqations,2000,165:165-174.
  • 9Byers R,Harris B J and Kwong M K.Weights means and oscillation of second order matrix differential system.J.Differential Eqations,1986,61:164-177.
  • 10Butler G J,Erbe L H and Mingarelli A B.Riccati techniques and variational principle in oscillatory theory for linear system.Trans.Amer.Math.Soc,1987,303:263-282.

引证文献1

数学学报（中文版）
2005年 第5期

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