广义中立型Emden-Fowler方程的振动准则

Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (6): 1067-1081.

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Oscillation Criteria for Generalized Neutral Emden-Fowler Equations

Zeng Yunhui¹, Luo Liping¹, Yu Yuanhong²

1. College of Mathematics and Statistics, Hengyang Normal University, Hunan Hengyang 421002;
2. Academy of System Sciences, Chinese Academy of Sciences, Beijing 100190

Received:2016-07-07 Revised:2016-11-08 Online:2016-12-26 Published:2016-12-26
Supported by:
Supported by the Construct Program of the Key Discipline in Hunan Province ([2016]) and the Natural Science Foundation of Education Department of Hunan Province (14C0170)

Abstract

Abstract:

Oscillation criteria are established for generalized neutral Emden-Fowler equations of the form
(r(t)|y'(t)|^α-1y'(t))'+f(t,x(σ(t)))=0, t≥t₀,
where α>0,y(t)=x(t)+p(t)x(τ(t)),-μ≤p(t)≤1,μ∈(0,1). Our results improve and extend some known results in the literature, recently. Some illustrating examples are also provided to show the importance of our results.

Key words: Emden-Fowler equation, Half-linear differential equation, Riccati method, Oscillation criterion

CLC Number:

O175.27

Zeng Yunhui, Luo Liping, Yu Yuanhong. Oscillation Criteria for Generalized Neutral Emden-Fowler Equations[J].Acta mathematica scientia,Series A, 2016, 36(6): 1067-1081.

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References

[1] Baculikova B, Li T X, Dgurina J. Oscillation theorems for second-order super-linear Neutral differential equations. Mathematica Slovaca, 2013, 63:123-134
[2] Dong J G. Oscillation behavior of second order nonlinear differential equations with deviating arguments. Comput Math Appl, 2010, 59:3710-3717
[3] Dzurina J, Stavroulakis I P. Oscillation criteria for second order delay differential equations. Appl Math Comput, 2003, 140:445-453
[4] Han Z, Li T, Sun S, Chen W. Oscillation of second order quasi-linear neutral delay differential equations. J Appl Math Comput, 2012, 40:143-152
[5] Li W T. Interval oscillation of second-order half-linear functional differential equations. Appl Math Comput, 2004, 155:451-468
[6] Liu L H, Bai Y Z. New oscillation criteria for second-order nonlinear neutral delay differential equations. J Comput Appl Math, 2009, 231:657-663
[7] Manojlovic J V. Oscillation criteria for second-order half-linear differential equations. Math Comput Modelling, 1999, 30:109-119
[8] Sun Y G, Meng F W. Note on the paper of Dyurina and Stavroulakis. Appl Math Comput, 2006, 174:1634-1641
[9] Wang Q R. Oscillation and asymptotics for second-order half-linear differential equations. Appl Math Comput, 2001, 122:253-266
[10] Ye L H, Xu Z T. Oscillation criteria for second order quasi-linear neutral delay differential equations. Appl Math Comput, 2009, 207:388-396
[11] Agarwal R P, Shieh S L, Yeh C C. Oscillation criteria for second-order retarded differential equations. Comput Math Appl, 2011, 62:4472-4478
[12] Baculikova B, Dzurina J. Oscillation theorems for second order nonlinear neutral differential equations. Comput Math Appl, 2011, 62:4472-4478
[13] Bohner M, Saker S H. Oscillation of damped second order nonlinear delay differential equations of Emden-Fowler type. Adv Dynamical Systems Appl, 2006, 1:163-182
[14] Erbe L, Hassan T S, Peterson A. Oscillation of second order neutral delay differential equations. Adv Dynamical Systems Appl, 2008, 3:53-71
[15] Li T X, Han Z L, Zhang C H, Sun S R. On the oscillation of second order Emdem-Fowler neutral differential equations. J Appl Math Comput, 2011, 37:601-610
[16] Saker S H. Oscillation of second order neutral delay differential equations of Emden-Fowler type. Acta Math Hungar, 2003, 100:37-62
[17] Tiryaki A. Oscillation criteria for a certain second order nonlinear differential equations with deviating arguments. Electronic J QTDE, 2009, 61:1-11
[18] Xu Z T. Oscillation theorems related to averaging technique for second order Emden-Fowler type neutral differential equations. Rocky Mount J Math, 2008, 38:649-667
[19] Liu H D, Meng F W, Liu P C. Oscillation and asymptotic analysis on a generalized Emden-Fowler equation. Appl Math Comput, 2012, 219:2739-2748
[20] Hale J K. Theory of Functional Differential Equations. New York:Springer-Verlag, 1977
[21] Driver D R. A mixed neutral systems. Nonlinear Anal, 1984, 8:155-158

Oscillation Criteria for Generalized Neutral Emden-Fowler Equations

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