时间测度链上具正负系数的二阶阻尼动力方程的振动准则

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Oscillation Criteria for Second-Order Dynamic Equations with Positive and Negative Coefficients and Damping on Time Scales

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Abstract:

The oscillation for certain second-order nonlinear variable delay dynamic equations with positive and negative coefficients and damping and nonlinear neutral on time scales is discussed. By using the time scales theory and the generalized Riccati transformation and the inequality technique, we establish some new oscillation criteria for the inequations. Our results extend and improve some known results, but also unify the oscillation of second-order nonlinear delay differential equations with damping and second-order nonlinear delay difference equations with damping.

Key words: Oscillation, Dynamic equations, Time scales, Positive and negative coefficients, Damping, Nonlinear neutral

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34k11

YANG Jia-Shan. Oscillation Criteria for Second-Order Dynamic Equations with Positive and Negative Coefficients and Damping on Time Scales[J].Acta mathematica scientia,Series A, 2014, 34(2): 393-408.

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[1] Hilger S. Analysis on measure chains-a unified approach to continuous and discrete calculus. Results Math, 1990, 18: 18--56

[2] Agarwal R P, Grace S R, O'Regan D. Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and
Sublinear Dynamic Equations. Dordrecht: Kluwer Academic, 2002

[3] Agarwal R P, Bohner M, Grace S R, et al. Discrete Oscillation Theory. New York: Hindawi Publishing Corporation, 2005

[4] Bohner M, Peterson A. Dynamic Equations on Time Scales: An Introduction with Applications. Boston: Birkhauser, 2001

[5] Bohner M, Peterson A. Advances in Dynamic Equations on Time Scales. Boston: Birkhauser,2003

[6] Agarwal R P, Bohner M, O'Regan D, et al. Peterson, Dynamic equations on time scales: a survey. J Comput Appl Math, 2002, 141: 1--26

[7] Bohner M, Saker S H. Oscillation of second order nonlinear dynamic equations on time scales. Rocky Mountain J Math, 2004, 34: 1239--1254

[8] Erbe L. Oscillation criteria for second order linear equations on a time scale. Can Appl Math Q, 2001, 9: 345--375

[9] Erbe L, Peterson A, Rehák P. Comparison theorems for linear dynamic equations on time scales. J Math Anal Appl, 2002, 275: 418--438

[10] Sun S, Han Z, Zhang C, Oscillation of second order delay dynamic equations on time scales. J Appl Math Comput, 2009, 30: 459--468

[11] Grace S R, Agarwal R P, Kaymakcalan B, et al. Oscillation theorems for second order nonlinear dynamic equations.
J Appl Math Comput, 2010, 32: 205--218

[12] Agarwal R P, Bohner M, Saker S H. Oscillation of second order delay dynamic equations. Can Appl Math Q, 2005, 13: 1--18

[13] Sahiner Y. Oscillation of second order delay differential equations on time scales. Nonlinear Anal TMA, 2005, 63: 1073--1080

[14] Saker S H. Oscillation criteria of second-order half-linear dynamic equations on time scales. J Comput Appl Math, 2005, {\bf 177}: 375--387

[15] Erbe L, Peterson A, Saker S H. Oscillation criteria for second order nonlinear delay dynamic equations. J Math Anal Appl, 2007, 333: 505--522

[16] Erbe L, Hassan T S, Peterson A. Oscillation criteria for nonlinear functional neutral dynamic equations on time scales. J Difference Equ Appl, 2009, 15(11/12): 1097--1116

[17] Grace S R, Bohner M, Agarwal R P. On the oscillation of second-order half-linear dynamic equations. J Difference Equ Appl, 2009, 15(5): 451--460

[18] Agarwal R P, Bohner M, Li W T. Nonoscillation and Oscillation: Theory for Functional Differential Equations. New York:Marcel Dekker, 2004.

[19] Tuna A, Kutukcu S. Some integral inequalities on time scales. Applied Mathematics and Mechanics, 2008, 29(1): 23--29

[20] Bohner M. Some oscillation criteria for first order delay dynamic equations. Far East J Appl Math, 2005, 18(3): 289--304

[21] Zhang Q X. Oscillation of second-order half-linear delay dynamic equations with damping on time scales. Journal of Computational and Applied, 2011, 235: 1180--1188

[22] 张全信, 高丽, 刘守华. 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(II). 中国科学: 数学, 2011, 41(10): 885--896

[23] 杨甲山. 时间测度链上一类具阻尼项的二阶动力方程的振动准则. 上海交通大学学报, 2012, 46(9): 1529--1533

[24] 欧柳曼, 朱思铭.时标动力方程的稳定性分析. 数学物理学报,2008, 28A(2): 308--319

[25] 杨甲山. 时间测度链上具非线性中立项的二阶动力方程的振动性. 中国科学院研究生院学报, 2012, 29(6): 731--737

[26] 李同兴, 韩振来, 张承慧, 等.时间尺度上三阶Emden-Fowler动力方程的振动准则. 数学物理学报,2012, 32A(1): 222--232

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