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时间模上一类二阶非线性动态方程的振动结果 被引量：8

Oscillation results of certain second-order nonlinear dynamic equations on time scales
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摘要 研究时间模上一类非线性的二阶中立型时滞动态方程的振动性,利用时间模上的理论和一些分析技巧,借助Riccati变换和H函数的方法,得到该方程振动的几个新的充分条件,改善了对方程的条件限制,推广和改进了现有文献中的有关结果,并给出例子说明结论的重要性. The oscillation for a certain class of second-order nonlinear neutral delay dynamic equations on time scales was discussed.Based on the time scales theory and some necessary analytic techniques,and generalized Riccati transformation and the method of H function,some new sufficient conditions for the oscillation of the equations were obtained.Our results could improve the restriction of the conditions for the equation.Some existing results in the literature were improved and extended.Some examples were given to illustrate the importance of our results.
作者 杨甲山 莫协强
机构地区 梧州学院数理系
出处 《安徽大学学报（自然科学版）》 CAS 北大核心 2015年第1期1-7,共7页 Journal of Anhui University(Natural Science Edition)
基金 国家自然科学基金资助项目(11071222) 湖南省自然科学基金资助项目(12JJ6006) 湖南省科技厅基金资助项目(2012FJ3107) 湖南省教育厅科研重点项目(09A082) 广西省教育厅科研基金资助项目(2013YB223)
关键词 振动性 时间模 中立型时滞动态方程 非线性中立项 oscillation time scales neutral delay dynamic equations nonlinear neutral term
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献20

  • 1Ravi P,Agarwal R P,Bohner M,et al.Nonoscillation and oscillation:theory for functional differential equations[M].New York:Marcel Dekker,2004.
  • 2Bohner M,Peterson A.Dynamic equations on time scales,an introduction with applications[M].Boston:Birkhauser,2001.
  • 3Agarwal R P,Bohner M,Grace S R,et al.Discrete oscillation theory[M].New York:Hindawi Publishing Corporation,2005.
  • 4Zhang Q X,Gao L.Oscillation criteria for second-order half-linear delay dynamic equations with damping on time scales[J].Sci Sin Math,2010,40(7):673-682.
  • 5Sahiner Y.Oscillation of second order delay differential equations on time scales[J].Nonlinear Analysis,TMA,2005,63:e1073-e1080.
  • 6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
  • 7Sun S,Han Z,Zhang C.Oscillation of second order delay dynamic equations on time scales[J].J Appl Math Comput,2009,30:459-468.
  • 8Grace 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.
  • 9Agarwal 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.
  • 10Saker S H.Oscillation of second-order nonlinear neutral delay dynamic equations on time scales[J].J Comput Appl Math,2006,187:123-141.

二级参考文献21

  • 1HILGER S. Analysis on measure chains- a unified approach to continuous and discrete calculus [ J ]. Results Math, 1990,18 : 18 -56.
  • 2BOHNER M,PETERSON A. Dynamic Equations on Time Scales, An Introduction with Applications [ M ]. Boston: Birkhauser, 2001.
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  • 4SAKER S H. Oscillation of nonlinear dynamic equations on time scales[ J ]. Appl Math Comput, 2004,148 ( 1 ) : 81 -91.
  • 5AGARWAL 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.
  • 6BOHNER M, SAKER S H. Oscillation of second order nonlinear dynamic equations on time scales [ J ]. Rocky Mountain J Math, 2004, 34(4) : 1239 -1254.
  • 7MEDICO A, KNOG Q. New Kamenev-type oscillation criteria for second-order differential equations on a meas- ure chain[J]. Computers Math Applic, 2005, 50:1211 - 1230.
  • 8SAHINER Y. Oscillation of second-order delay differential equations on time scales [ J ]. Nonlinear Analysis, TMA, 2005,63 : e1073 - el080.
  • 9ZHANG B G, DENG X H. Oscillation of delay differential equations on time scales [ J ]. Math Comput Model- ling,2002, 36( 11 ) : 1307 - 1318.
  • 10AGARWAL R P, BOHNER M, Saker S H. Oscillation of second order delay dynamic equations [ J ]. Canadian Applied Mathematics Quarterly, 2005, 13( 1 ) : 1 - 18.

共引文献38

同被引文献88

引证文献8

二级引证文献27

安徽大学学报（自然科学版）
2015年 第1期

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