具非线性中立项的广义Emden-Fowler微分方程的振动性

Abstract

Abstract: We study the oscillatory behavior of a certain class of second-order nonlinear variable delay generalized Emden-Fowler functional differential equations with a nonlinear neutral term of the form
{a(t)|[x(t)+p(t)x^α(τ(t))]'|^β-1[x(t)+p(t)x^α(τ(t))]'}'+q(t)f(|x(δ(t))|^γ-1x(δ(t)))=0(t ≥ t₀). By using the generalized Riccati transformation and Bernoulli's inequality and Yang's inequality, we establish some new oscillation criteria for the equations under the cases when
∫_t₀^+∞ a^-1/β(t)dt=+∞ and ∫_t₀^+∞ a^-1/β(t)dt < +∞,
the results obtained extend and improve some related results reported in the literature. Examples are provided to illustrate assumptions in our theorems are less restrictive.

Key words: Oscillation, Functional differential equation, Nonlinear neutral, Riccati transformation

CLC Number:

O175.1

Zhang Xiaojian. Oscillation of Generalized Emden-Fowler Differential Equations with Nonlinear Neutral Term[J].Acta mathematica scientia,Series A, 2018, 38(4): 728-739.

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References 17

[1]	Agarwal R P, Bohner M, Li W T. Nonoscillation and Oscillation:Theory for Functional Differential Equations. New York:Marcel Dekker, 2004
[2]	Hasanbulli M, Rogovchenko Yu V. Oscillation criteria for second order nonlinear neutral differential equations. Appl Math Comput, 2010, 215:4392-4399
[3]	Li T, Agarwal R P, Bohner M. Some oscillation results for second-order neutral differential equations. J Indian Math Soc, 2012, 79:97-106
[4]	Lin X, Tang X. Oscillation of solutions of neutral differential equations with a superlinear neutral term. Appl Math Lett, 2007, 20:1016-1022
[5]	Han Z, Li T, Sun S, et al. Remarks on the paper. Appl Math Comput, 2009, 207:388-396; Appl Math Comput, 2010, 215:3998-4007
[6]	Sun Y G, Meng F W. Note on the paper of Dzurina and Stavroulakis. Appl Math Comput, 2006, 174:1634-1641
[7]	黄记洲, 符策红. 广义Emden-Fowler方程的振动性. 应用数学学报,2015, 38(6):1126-1135 Huang Jizhou, Fu Cehong. Oscillation criteria of generalized Emden-Fowler equations. Acta Mathematicae Applicatae Sinica, 2015, 38(6):1126-1135
[8]	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 Yunhui, Luo liping, Yu Yuanhong. Oscillation for Emden-Fowler delay differential equations of neutral type. Acta Mathematica Scientia, 2015, 35A(4):803-814
[9]	Li T, Rogovchenko Yu V, Zhang C. Oscillation of second-order neutral differential equations. Funkc Ekvac, 2013, 56:111-120
[10]	Sun S, Li T,Han Z, et al. Oscillation theorems for second-order quasilinear neutral functional differential equations. Abstract and Applied Analysis, 2012, 2012:1-17
[11]	Zhong J, Ouyang Z, Zou S. An oscillation theorem for a class of second-order forced neutral delay differential equations with mixed nonlinearities. Applied Mathematics Letters, 2011, 24(8):1449-1454
[12]	Sun S, Li T, Han Z, et al. On oscillation of second-order nonlinear neutral functional differential equations. Bull Malays Math Sci Soc, 2013, 36(3):541-554
[13]	Yang J S, Qin X W, Zhang X J. Oscillation criteria for certain second-order nonlinear neutral delay dynamic equations with damping on time scales. Mathematica Applicata, 2015, 28(2):439-448
[14]	杨甲山. 具非线性中立项的二阶变时滞微分方程的振荡性. 华东师范大学学报(自然科学版), 2016, 2016(4):30-37 Yang Jiashan. Oscillation of second-order variable delay differential equations with nonlinear neutral term. Journal of East China Normal University (Natural Science), 2016, 2016(4):30-37
[15]	杨甲山, 覃桂茳. 一类二阶微分方程新的Kamenev型振动准则. 浙江大学学报(理学版), 2017,44(3):274-280 Yang Jiashan, Qin Guijiang. Kamenev-type oscillation criteria for certain second-order differential equations. Journal of Zhejiang University (Science Edition), 2017, 44(3):274-280
[16]	杨甲山. 具阻尼项的二阶Emden-Fowler型泛函差分方程的振动性. 华中师范大学学报(自然科学版), 2017, 51(6):723-730 Yang Jiashan. Oscillation criteria for second-order Emden-Fowler functional difference equations with damping. Journal of Central China Normal University(Natural Sciences), 2017, 51(6):723-730
[17]	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 Wenjuan, Tang Huo, Yu Yuanhong. Oscillation of the neutral Emden-Fowler differential equation. Acta Mathematica Scientia, 2017, 37A(6):1062-1069

Oscillation of Generalized Emden-Fowler Differential Equations with Nonlinear Neutral Term

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