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具有分布时滞的二阶非线性中立型时标动力方程的振动定理 被引量：9

OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR NEUTRAL DYNAMIC EQUATIONS ON TIME SCALES WITH DISTRIBUTED DELAY
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摘要 利用广义Riccati变换技术,研究时标上具有分布时滞的二阶非线性中立型动力方程的振动性,其中β>0是两个正奇数之比,获得了方程所有解振动的几个充分条件,推广和改进了一些已知的结果,并给出了几个应用实例. This paper is concerned with the oscillation of the second-order nonlinear neutral dynamic equation with distributed delay （r（t）（（y（t）＋p（t）y（τ（t）））△）β）△＋∫^d c F（t,ξ,y（δ（t,ξ）））△ξ=0 on an arbitrary time scale T,whereβ0 is a quotient of odd positive integers.By employing the generalized Riccati transformation technique,several sufficient conditions for all solutions of the equation be oscillatory.The results extend and improve some known results.Some examples to illustrate the main results are given.
作者 陈大学 刘洁纯
机构地区 湖南工程学院理学院 湖南工程学院成人教育学院
出处 《系统科学与数学》 CSCD 北大核心 2010年第9期1191-1205,共15页 Journal of Systems Science and Mathematical Sciences
基金 湖南省教育厅资助科研(06C242) 湖南省科技计划(2010FJ6021)项目资助
关键词 振动定理 二阶非线性中立型动力方程 分布时滞 时标 广义Riccati变换 Oscillation theorem second-order nonlinear neutral dynamic equation distributed delay time scale generalized Riccati transformation
分类号 O175 [理学—基础数学]
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参考文献15

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同被引文献50

  • 1刘爱莲,吴洪武,朱思铭,Ronald M.Mathsen.OSCILLATION FOR NONAUTONOMOUS NEUTRAL DYNAMIC DELAY EQUATIONS ON TIME SCALES[J].Acta Mathematica Scientia,2006,26(1):99-106. 被引量：6
  • 2Zhang B G,Zhu Shanliang.Oscillation of second-order nonlinear delay dynamic equations on time scales[J].Comp Math Appl,2005,49:599-609.
  • 3Saker S H,Agarwal R P,O'Regan D.Oscillation results for second order nonlinear neutral delay dynamic equations on time scales[J].Appl Anal,2007,86:1-17.
  • 4Jia Baoguo,Erbe L,Peterson A.Oscillation of a family of qdifference equations[J].Appl Math Letters,2009,22:871-875.
  • 5Saker S H,Agarwal R P,O'Regan D.Oscillation of secondorder damped dynamic equations on time scales[J].J Math Anal Appl,2007,330:1317-1337.
  • 6Erbe L,Peterson A,Saker S H.Oscillation criteria for second-order nonlinear delay dynamic equations[J].J Math Anal Appl,2007,333:505-522.
  • 7Agarwal R P,O'Regan D,Saker S H.Oscillation criteria for second-order nonlinear neutral delay dynamic equations[J].J Math Anal Appl,2004,300:203-217.
  • 8Wu H W,Zhang R K,Mathsen R M.Oscillation criteria for second-order nonlinear neutral variable delay dynamic equations[J].Appl Math Comput,2006,178:321-331.
  • 9Sun Y G,Wong J S W.Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities[J].J Math Anal Appl,2007,334:549-560.
  • 10HILGER S. Analysis on measure chains-a unified approach to continuous and discrete calculus[J].Results in Mathematics,1990.18-56.

引证文献9

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系统科学与数学
2010年 第9期

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