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时间测度链上一类二阶动力方程的振动性 被引量：4

Oscillation of a Class of Second-order Dynamic Equation on Time Scales
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摘要 研究了时间测度链上的一类具有非线性中立项和变时滞的二阶非线性动力方程的振动性.通过引入参数函数和广义的Riccati变换,并借助时间测度链上的有关理论,得到了方程振动的几个充分条件.所得结果推广和改进了现有文献中相应的结果. In this paper, the oscillation for a class of second order nonlinear dynamic equation on time scales with nonlinear neutral term and variable delay was discussed. Using the time scales theory and some necessary analytic techniques, some sufficient conditions for oscillation of the equation were proposed by introducing parameter function and the generalized Riccati transformation. These results improve and generalize some corresponding known results in the literature.
作者 杨甲山 苏芳
机构地区 梧州学院数理系
出处 《数学的实践与认识》 CSCD 北大核心 2014年第13期265-270,共6页 Mathematics in Practice and Theory
基金 广西教育厅科研项目(2013YB223) 湖南省教育厅科研重点项目(09A082)
关键词 时间测度链 动力方程 非线性中立项 RICCATI变换 振动性 time scales dynamic equations nonlinear neutral term Riccati transformation oscillation
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献12

  • 1罗李平,彭白玉.非线性脉冲中立型时滞抛物方程解的振动性质[J].数学的实践与认识,2009,39(13):174-179. 被引量：7
  • 2杨甲山,李继猛.带最大值项的二阶非线性差分方程的振动性定理[J].安徽大学学报（自然科学版）,2012,36(3):19-22. 被引量：6
  • 3Hilger S. Analysis on measure chains-a unified approach to continuous and discrete calculus[J]. Results Math, 1990, 18: 18-56.
  • 4Bohner M, Peterson A. Dynamic equations on time scales, an introduction with applications[M]. Boston: Birkhauser, 2001.
  • 5Agarwal R P,Bohner M,O ' Regan D,et al.Dynamic equations on time scales: a survey[J]. J Comput Appl Math, 2002, 141(1-2): 1-26.
  • 6Sahiner Y. Oscillation of second order delay differential equations on time scales [J]. Nonlinear Analysis, TMA, 2005, 63: e1073-e1080.
  • 7Zhang Q X, Gao L. Oscillation criteria for second-order half-linear delay dynamic equations with damping on time scales (in Chinese)[J]. Sci Sin Math, 2010, 40(7): 673-682.
  • 8杨甲山,刘兴元.时间测度链上二阶动力方程的振动性定理(英文)[J].安徽大学学报（自然科学版）,2013,37(1):8-12. 被引量：5
  • 9Agarwal R P, Bohner M, Saker S H.Oscillation of second order delay dynamic equations [J]. Cana- dian Applied Mathematics Quarterly, 2005, 13(1): 1-18.
  • 10Zhang B G, Zhu Shan-liang.Oscillation of second order nonlinear delay dynamic equations on time scales[J]. Computers Math Applic, 2005, 49(4): 599-609.

二级参考文献42

  • 1范彩霞,赵爱民,邓嵩.带有极大值项的中立型差分方程的振动性[J].山西大学学报（自然科学版）,2005,28(1):5-7. 被引量：10
  • 2薛秋条,徐德义,刘安平.非线性脉冲时滞双曲偏微分方程的振动性[J].武汉理工大学学报,2005,27(6):52-54. 被引量：8
  • 3Ethiraju Thandapani,刘召爽,李巧銮,Sebastian Elizabeth.含最大值项二阶中立型差分方程的渐近性(英文)[J].Journal of Mathematical Research and Exposition,2006,26(2):191-198. 被引量：3
  • 4Agarwal R P,Bohner M,Li Wantong.Nonoscillation and Oscillation:Theory for Functional Differential Equations[M].New York:Marcel Dekker,2004.
  • 5Hilger S.Analysis on measure chains-a unified approach to continuous and discrete calculns[J].Results in Mathematics,1990,18:18-56.
  • 6Bohner M,Peterson A.Dynamic Equations on Time Scales,an Introduction with Applications[M].Boston:Birkhauser,2001.
  • 7Agarwal R P,Bohner M,O'Regan D,et al.Dynamic equations on time scales:a survey[J].Journal of Computational and Applied Mathematics,2002,141(1-2):1-26.
  • 8Sahiner Y.Oscillation of second order delay differential equations on time scales[J].Nonlinear Analysis,TMA,2005,63:e1073-e1080.
  • 9Agarwal R P,Bohner M,Saker S H.Oscillation of second order delay dynamic equations[J].Canadian Applied Mathematics Quarterly,2005,13(1):1-18.
  • 10Zhang Binggen,Deng Xinghua.Oscillation of delay differential equations on time scales[J].Computational Mathematics and Modeling,2002,36(11):1307-1318.

共引文献42

同被引文献61

  • 1杨甲山.时间测度链上具非线性中立项的二阶阻尼动力方程的振动性[J].浙江大学学报（理学版）,2012,39(3):261-265. 被引量：13
  • 2潘元元,韩振来.时标上二阶中立型时滞动力方程的振动性[J].济南大学学报（自然科学版）,2012,26(2):191-194. 被引量：5
  • 3韩振来,时宝,孙书荣.时间尺度上二阶时滞动力方程的振动性[J].中山大学学报（自然科学版）,2007,46(6):10-13. 被引量：29
  • 4BOHNER M, PETERSON A. Dynamic Equations on Time Scales, An Introduction with Applications [M]. Boston: Birkhauser, 2001.
  • 5AGARWAL R P, BOHNER M, GRACE S R, et al. Discrete Oscillation Theory [M]. New York: Hindawi Publishing Corporation, 2005.
  • 6ZHANG Q X, GAOL. Oscillation criteria for second-order half-linear delay dynamic equations with damping on time scales [J]. Sci Sin Math, 2010, 40(7): 673-682.
  • 7SAHINER Y. Oscillation of second order delay differential equations on time scales [J]. Nonlinear Analysis, TMA, 2005, 63: e1073-e1080.
  • 8SUN S, HAN Z, ZHANG C. Oscillation of second order delay dynamic equations on time scales [J]. J Appl Math Comput, 2009, 30: 459-468.
  • 9GRACE S R, AGARWAL R P, KAYMAKCALAN B, et al. Oscillation theorems for second order nonlinear dynamic equations [J]. J Appl Math Comput, 2010, 32: 205-218.
  • 10AGARWAL R P, O'REGAN D, SSKER S H. Oscillation criteria for second-order nonlinear neutral delay dynamic equations [J]. J Math Anal Appl, 2004, 300: 203-217.

引证文献4

二级引证文献21

数学的实践与认识
2014年 第13期

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