二阶非线性中立型时滞微分方程的振动性

Abstract

Abstract:

In this paper, the oscillatory behavior of solutions to a nonlinear second-order neutral differential equation is to study. Using double Riccati transformation and the technique of inequations, some new sufficient conditions are obtained for the solutions of all oscillations and the results generalize, improve and unify the oscillation theorems of half linear functional differential equations, nonlinear equations and generalized Emden-Fowler type equations in the literature recently. At last, some examples are given to illustrate the effectiveness of our results.

Key words: Second order nonlinear differential equation, Half linear differential equation, Emden-Fowler equation, Neutral, Riccati transformation, Oscillation criterion

CLC Number:

O175

Zhiyu Zhang,Yuanhong Yu,Shuping Li,Shizhu Qiao. Oscillation of Second Order Nonlinear Differential Equations with Neutral Delay[J].Acta mathematica scientia,Series A, 2019, 39(4): 797-811.

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References 27

[1]	Dzurina J, Stavroulakis I P. Oscillation criteria for second order delay differentional equations. Appl Math Comput, 2003, 140:445-453<br />
[2]	Sun Y G, Meng F W. Note on the paper of Dzurina and Stavroulakis. Appl Math Comput, 2006, 174:1634-1641<br />
[3]	Dong J G. Oscillation behavior of second-order nonlinear neutral differential equtions with deviating arguments. Comput Math Appl, 2010, 59:3710-3717<br />
[4]	Erbe L, Hassan T S, Peterson A. Oscillation of second-order neutral differential equations. Adv Dynam Syst Appl, 2008, 3:53-71<br />
[5]	Li T,Han Z, Zhang C, Sun S. On the oscillation of second order Emden-Fowler neutral differential equations. J Appl Math Comput, 2011, 37:601-610<br />
[6]	Liu H D, Meng F W, Liu P H. Oscillation and asymptotic analysis on a new generalized Emden-Fowler equation. Appl Math Comput, 2012, 219:2739-2748<br />
[7]	曾云辉, 罗李平, 俞元洪.中立型Emden-Fowler时滞微分方程的振动性.数学物理学报, 2015, 35A(4):803-814 Zeng Y H, Luo L P, Yu Y H. Oscillation for Emden-Fowler Delay differential equations of neutral type. Acta Math Sci, 2015, 35A(4):803-814<br />
[8]	Agarwal R P, Shieh S L, Yeh C C. Oscillation criteria for second order retarded differential equations. Math Comput Modelling, 1997, 26:1-11<br />
[9]	Baculikova B, Li T, Dzurina J. Oscillation theorems for second order supper-linear neutral differential equations. Math Slovaca, 2013, 63:123-134<br />
[10]	Liu L,Bai Y. New oscillation criteria for second order nonlinear delay neutral differential equations. J Comput Appl Math, 2009, 231:657-663<br />
[11]	Wang X L, Meng F W. Oscillation criteria of second order quasi-linear neutral delay differential equations. Math Comput Modelling, 2007, 46:415-421<br />
[12]	Xu R, Meng F W. Oscillation criteria for second order quasi-linear neutral delay differential equations. Appl Math Comput, 2007, 192:216-222<br />
[13]	Tiryaki A. Oscillation criteria for a certain second order nonlinear differential equations with deviating arguments. Electron J Qual Theory Differ Equa, 2009, 61:1-11<br />
[14]	Hasanbulli M, Rogovchenko Yu V. Oscillation criteria for second order nonlinear neutral differential equations. Appl Math Comput, 2010, 215:4392-4399<br />
[15]	Li T, Rogovchenko Yu V, Zhang C. Oscillation of second order nonlinear neutral differential equations. Funkc Ekvacioj, 2013, 56:111-120<br />
[16]	Ye L, Xu Z. Oscillation criteria for second order quasi-linear neutral delay differential equations. Appl Math Comput, 2009, 207:388-396<br />
[17]	Qin H, Shang N, Lu Y. A note on oscillation criteria of second order nonlinear neutral delay differential equations. Comput Math Appl, 2008, 56:2987-2992<br />
[18]	Lin X. Oscillation of second order nonlinear neutral differential equations. J Math Anal Appl, 2005, 309:442-452<br />
[19]	Karpuz B, Manojlovic J V, Ocalan O, Shoukaku Y. Oscillation criteria for a class of second order neutral delay differential equations. Appl Math Comput, 2009, 210:303-312<br />
[20]	Baculikova B, Dzurina J. Oscillation theorems for second order nonlinear neutral differential equations. Comput Math Appl, 2011, 62:4472-4478<br />
[21]	Leighton W. The detection of the oscillation of solutions of a second order linear differential equation. Duke Math J, 1950, 17:57-62<br />
[22]	Philos C G. Oscillation theorems for linear differential equations of second order. Arch Math, 1989, 53:482-492<br />
[23]	曾云辉, 罗李平, 俞元洪. 广义中立型Emden-Fowler方程的振动准则.数学物理学报,2016, 36A(6):1067-1081 Zeng Y H, Luo L P,Yu Y H. Oscillation criteria for generalized neutral Emden-Fowler equations. Acta Math Sci, 2016, 36A(6):1067-1081<br />
[24]	罗红英, 屈英, 俞元洪. 具有正负系数的二阶中立型时滞Emden-Fowler方程的振动准则.应用数学学报, 2017, 40A(5):667-675 Luo H Y,Qu Y,Yu Y H. Oscillation criteria of second order neutral delay Emden-Fowler equations with positive and negative coefficients. Acta Math Appl Sinica, 2017, 40A(5):667-675<br />
[25]	李文娟, 汤获, 俞元洪. 中立型Emden-Fowler微分方程的振动性.数学物理学报,2017, 37A(6):1062-1069 Li W J,Tang H, Yu Y H. Osillation of the Emden-Fowler differential equations.Acta Math Sci, 2017, 37A(6):1062-1069<br />
[26]	杨甲山, 李同兴. 时间模上一类二阶阻尼Emden-Fowler型动态方程的振荡性.数学物理学报,2018, 38A(1):134-155 Yang J S,Li T X. Osillation for a class of second-order damped Emden-Fowler dynamic equations on time scalas. Acta Math Sci, 2018, 38A(1):134-155<br />
[27]	张晓建. 具有非线性中立项的广义Emden-Fowler微分方程的振动性.数学物理学报,2018, 38A(4):728-739 Zhang X J. Osillation of generalized Emden-Fowler differential equations with nonlinear neutral term. Acta Math Sci, 2018, 38A(4):728-739

Oscillation of Second Order Nonlinear Differential Equations with Neutral Delay

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