二阶广义Emden-Fowler型延迟微分方程的振荡性分析

Abstract

Abstract:

We study the oscillatory behavior of a class of second-order generalized EmdenFowler-type nonlinear delay functional differential equations in this paper. By using a couple generalized Riccati transformation and some necessary analytic techniques, we establish some new oscillation criteria for the equations under both the cases canonical form and noncanonical form, which deal with some cases not covered by existing results in the literature. Three examples are given to illustrate the main results of this article.

Key words: Oscillation, Delay, Emden-Fowler-type differential equation, Riccati transformation

CLC Number:

O175.27

Jimeng Li. Oscillation Analysis of Second-Order Generalized Emden-Fowler-Type Delay Differential Equations[J].Acta mathematica scientia,Series A, 2019, 39(5): 1041-1054.

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References 12

1	Dzurina J , Stavrouakis I P . Oscillation criteria for second order delay differential equations. Appl Math Comput, 2003, 14 (3): 445- 453
2	Sun Y G , Meng F W . Note on the paper of Dzurina and Stavroulakis. Appl Math Comput, 2006, 27 (4): 1634- 1641
3	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 J Z , Fu C H . Oscillation criteria of generalized Emden-Fowler equations. Acta Mathematicae Applicatae Sinica, 2015, 38 (6): 1126- 1135
4	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 doi: 10.3969/j.issn.1003-3998.2015.04.016
	Zeng Y H , Luo L P , Yu Y H . Oscillation for Emden-Fowler delay differential equations of neutral type. Acta Mathematica Scientia, 2015, 35A (4): 803- 814 doi: 10.3969/j.issn.1003-3998.2015.04.016
5	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 doi: 10.3969/j.issn.1003-3998.2017.06.006
	Li W J , Tang H , Yu Y H . Oscillation of the neutral Emden-Fowler differential equation. Acta Mathematica Scientia, 2017, 37 (6): 1062- 1069 doi: 10.3969/j.issn.1003-3998.2017.06.006
6	Xing G J , Li T X , Zhang C H . Oscillation of higher-order quasi-linear neutral differential equations. Advances in Difference Equations, 2011, 2011: 45 doi: 10.1186/1687-1847-2011-45
7	杨甲山, 方彬. 二阶广义Emden-Fowler型微分方程的振荡性. 华中师范大学学报(自然科学版), 2016, 50 (6): 799- 804 doi: 10.3969/j.issn.1000-1190.2016.06.001
	Yang J S , Fang B . Oscillation of certain second-order generalized Emden-Fowler-type differential equations. Journal of Central China Normal University (Natural Sciences), 2016, 50 (6): 799- 804 doi: 10.3969/j.issn.1000-1190.2016.06.001
8	杨甲山. 二阶Emden-Fowler型非线性变时滞微分方程的振荡准则. 浙江大学学报(理学版), 2017, 44 (2): 144- 149
	Yang J S . Oscillation criteria of second-order Emden-Fowler nonlinear variable delay differential equations. Journal of Zhejiang University (Science Edition), 2017, 44 (2): 144- 149
9	Sun S R , Li T X , Han Z L , et al. On oscillation of second-order nonlinear neutral functional differential equations. Bull Malays Math Sci Soc, 2013, 36 (3): 541- 554
10	Ye L , Xu Z . Oscillation criteria for second order quasilinear neutral delay differential equations. Applied Mathematics and Computation, 2009, 207 (2): 388- 396 doi: 10.1016/j.amc.2008.10.051
11	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, 40 (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 Mathematicae Applicatae Sinica, 2017, 40 (5): 667- 675
12	杨甲山. 一类具有非线性中立项的二阶微分方程振动性. 东北师大学报(自然科学版), 2017, 49 (3): 13- 17
	Yang J S . Oscillation of certain second-order differential equations with nonlinear neutral term. Journal of Northeast Normal University (Natural Science Edition), 2017, 49 (3): 13- 17

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Oscillation Analysis of Second-Order Generalized Emden-Fowler-Type Delay Differential Equations

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