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线性时滞微分方程解的振动准则 被引量:1

Oscillation Criterions of Linear Delay Differential Equations
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摘要 建立线性时滞微分方程x (t) +∑ni=1 pi(t) x(t- τi(t) ) =0 ,  t≥ to的所有解振动的新准则。当 pi(t) ,τi(t) (i=1 ,2 ,… ,n)均为常数时 ,条件是充分必要的。 The aim of this paper is to study the oscillation for the linear delay differential equation, x(t)+∑ni=1p_i(t)x(t-τ_i(t))=0. Some new criterions are obtained for the oscillation of all solutions for the above equation. These conditions improve and extend some known results.
作者 武冬
出处 《青岛海洋大学学报(自然科学版)》 CSCD 北大核心 2002年第6期1023-1029,共7页 Journal of Ocean University of Qingdao
关键词 线性时滞微分方程 振动性 反证法 充要条件 delay differential equation oscillation solution
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参考文献3

  • 1[1]Phiols Ch G.Oscillation of first order linear differential equaton.[J] J Math Anal Appl, 1991,157 (1):17~33
  • 2[2]Ladde G S, Lakshmikantham V, Zhang B G. Oscillation Theory of Differential Equation, with Deviating Arguments. [M] N Y: Marcel, Dekker,1987
  • 3[3]Gyori I. On the oscillatory behaviour of solution of certain nonlinear and linear clifferential equation. [J] Nonlinear Analysis, 1984,8(5):429~439

同被引文献5

  • 1Philos Ch G. Oscillation of first order linear differential equaton[ J ]. J Math Anal Appl, 1991, 157 ( 1 ) : 17 - 33.
  • 2Ladas G, Stavroulakis I P. Oscillation criterions of linear delay differential equations [J]. Diff Eqs, 1982, (44) : 134 - 152.
  • 3Ladde G S,Lakshmikantham V,Zhang B G. Oscillation theory of differential equation with deviating arguments[ M]. New york: Marcel,Dekker, 1987.
  • 4Gyori I. On the oscillatory behaviour of solution of certain nonlinear and linear differential equation[ J]. Nonlinear Analysis, 1984,8(5) :429 - 439.
  • 5张炳根.泛函微分方程振动理论的发展[J].科学通报,1998,43(4):345-354. 被引量:29

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