Oscillation of second-order nonlinear variable delay dynamic equations with nonlinear neutral term on time scales is discussed. By using the time scale theory and some necessary analytic techniques and by introducing parameter functions and the generalized Riccati transformation, some sufficient conditions for the oscillation of the equations are obtained. Some examples are given to illustrate our main conclusions.
YANG Jia-Shan
. Oscillation of second-order dynamic equations with nonlinear neutral term on time scales[J]. Journal of University of Chinese Academy of Sciences, 2012
, (6)
: 731
-737
.
DOI: 10.7523/j.issn.2095-6134.2012.6.002
[1] Hilger S. Analysis on measure chains-a unified approach to continuous and discrete calculus[J]. Results Math, 1990, 18: 18-56.
[2] Bohner M, Peterson A. Dynamic equations on time scales, an introduction with applications[M]. Boston: Birkhauser, 2001.
[3] Agarwal 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.
[4] Sahiner Y. Oscillation of second order delay differential equations on time scales [J]. Nonlinear Analysis, TMA, 2005, 63: e1073-e1080.
[5] Zhang 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 (in Chinese). 张全信, 高丽. 时间尺度上具阻尼项的二阶半线性时滞动力方程的振动准则[J]. 中国科学: 数学, 2010, 40(7): 673-682.
[6] Agarwal R P, Bohner M, Li W T. Nonoscillation and oscillation: Theory for functional differential equations[M]. New York: Marcel Dekker, 2004.
[7] Agarwal R P, Bohner M, Saker S H. Oscillation of second order delay dynamic equations[J]. Canadian Applied Mathematics Quarterly, 2005, 13(1): 1-18.
[8] Han Z L, Shi B, Sun S R. Oscillation of second-order delay dynamic equation on time scales[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2007, 46(6): 10-13 (in Chinese). 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.
[9] Han Z L, Sun S R, Yang D W.Kamenev-type oscillation criteria for second-order nonlinear delay dynamic equations on time scales[J]. Journal of Shandong University:Natural Science, 2006, 41(6): 16-19(in Chinese). 韩振来, 孙书荣, 杨殿武. 时间尺度上二阶非线性时滞动力方程的Kamenev振动准则[J]. 山东大学学报:理学版, 2006, 41(6): 16-19.
[10] Yang J S. Oscillation for a class of second-order nonlinear dynamic equation on time scales[J]. Journal of Sichuan University: Natural Science Edition, 2011, 48(2): 278-282(in Chinese). 杨甲山. 时间测度链上一类二阶非线性动力方程的振动性[J]. 四川大学学报:自然科学版, 2011, 48(2): 278-282.
[11] Yang J S, Fang B. Oscillation criteria of a class of second-order dynamic equations on time scales[J]. Applied Mathematics A Journal of Chinese Universities(Ser A), 2011, 26(2): 149-157(in Chinese). 杨甲山, 方彬. 时间测度链上一类二阶动力方程的振动准则[J]. 高校应用数学学报, 2011, 26(2): 149-157.
[12] Sun S R, Han Z L, Zhang C H.The oscillation criteria of second-order eEmden-Fowler neutral delay dynamic equations on time scales [J]. Journal of Shanghai Jiaotong University, 2008, 42(12): 2070-2075(in Chinese). 孙书荣, 韩振来, 张承慧. 时间尺度上二阶Emden-Fowler中立型时滞动力方程的振动准则[J]. 上海交通大学学报, 2008, 42(12): 2070-2075.
[13] Li T X, Han Z L.Oscillation for second-order superlinar dynamic equations on time scales[J]. Journal of University of Jinan:Science and Technology, 2010, 24(2): 209-211(in Chinese). 李同兴, 韩振来. 时间尺度上二阶超线性动力方程振动性[J]. 济南大学学报:自然科学版, 2010, 24(2): 209-211.
[14] Sun Y B, Han Z L, Li T X. Oscillation criteria for second-order quasilinear neutral dynamic equations[J]. Journal of University of Jinan:Science and Technology, 2010, 24(3): 308-311(in Chinese). 孙一冰, 韩振来, 李同兴. 二阶拟线性中立型动力方程振动准则[J]. 济南大学学报:自然科学版, 2010, 24(3): 308-311.
[15] Zhang G R, Sun S R. Oscillation for second-order nonlinear delay dynamic equations[J]. Journal of University of Jinan:Science and Technology, 2010, 24(4): 414-416(in Chinese). 张光荣, 孙书荣. 二阶非线性时滞动力方程的振动性[J]. 济南大学学报:自然科学版, 2010, 24(4): 414-416.
