Back
 JAMP  Vol.3 No.9 , September 2015
Oscillation of Second Order Nonlinear Neutral Differential Equations with Mixed Neutral Term
Abstract: In this paper, we obtained some sufficient conditions for the oscillation of all solutions of the second order neutral differential equation of the form where , and . Examples are provided to illustrate the main results.
Cite this paper: Arul, R. and Shobha, V. (2015) Oscillation of Second Order Nonlinear Neutral Differential Equations with Mixed Neutral Term. Journal of Applied Mathematics and Physics, 3, 1080-1089. doi: 10.4236/jamp.2015.39134.
References

[1]   Bainov, D.D. and Mishev, D.P. (1991) Oscillation Theory of Neutral Differential Equations with Delay. Adam Hilger, Bristol.

[2]   Gyori, I. and Ladas, G. (1991) Oscillation Theory of Delay Differential Equations with Applications. Claredon Press, Oxford.

[3]   Hale, J. (1977) Theory of Functional Differential Equations. Springer, New York.
http://dx.doi.org/10.1007/978-1-4612-9892-2

[4]   Agarwal, R.P. and Grace, S.R. (1999) Oscillation Theorems for Certain Neutral Functional Differential Equations. Computers & Mathematics with Applications, 38, 1-11.
http://dx.doi.org/10.1016/S0898-1221(99)00280-1

[5]   Driver, R.D. (1984) A Mixed Neutral System. Nonlinear Analysis, 8, 155-158.
http://dx.doi.org/10.1016/0362-546X(84)90066-X

[6]   Dzurina, J., Busa, J. and Airyan, E.A. (2002) Oscillation Criteria for second Order Differential Equations of Neutral Type with Mixed Arguments. Differential Equation, 38, 137-140.

[7]   Dzurina, J. and Stavroulakis, I.P. (2003) Oscillation Criteria for Second Order Delay Differential Equations. Applied Mathematics and Computation, 140, 445-453.
http://dx.doi.org/10.1016/S0096-3003(02)00243-6

[8]   Grace, S.R. (1992) Oscillation Theorems for Nonlinear Differential Equations of Second Order. Journal of Mathematical Analysis and Applications, 171, 220-241.
http://dx.doi.org/10.1016/0022-247X(92)90386-R

[9]   Grace, S.R. (1995) On the Oscillation of Mixed Neutral Equations. Journal of Mathematical Analysis and Applications, 194, 377-388.
http://dx.doi.org/10.1006/jmaa.1995.1306

[10]   Grace, S.R. (1995) Oscillation of Mixed Neutral Functional Differential Equations. Applied Mathematics and Computation, 68, 1-13.
http://dx.doi.org/10.1016/0096-3003(94)00075-F

[11]   Grammatikopouls, M.K., Ladas, G. and Meimaridou, A. (1985) Oscillation of Second Order Neutral Delay Differential Equations. Radovi Matematicki, 1, 267-274.

[12]   Han, Z.L., Li, T.X., Sun, S.R. and Chen, W.S. (2010) On the Oscillation of Second Order Neutral Delay Differential Equations. Advances in Difference Equations, 2010, Article ID: 289340.

[13]   Karpuz, B., Manojlovic, J.V., Ocalan, O. and Shoukaku, Y. (2009) Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations. Applied Mathematics and Computation, 210, 303-312.
http://dx.doi.org/10.1016/j.amc.2008.12.075

[14]   Li, T.X., Rogovchenko, Y.V. and Zhang, C.H. (2013) Oscillation of Second Order Neutral Differential Equations. Funkcialaj Ekvacioj, 56, 111-120.
http://dx.doi.org/10.1619/fesi.56.111

[15]   Li, T.X. and Thandapani, E. (2014) Oscillation of Solutions to Second Order Neutral Differential Equations. Electronic Journal of Differential Equations, 2014, 1-7.

[16]   Liu, L.H. and Bai, Y.Z. (2009) New Oscillation Crieria for Second Order Nonlinear Neutral Delay Differential Equations. Journal of Computational and Applied Mathematics, 231, 657-663.

[17]   Liu, X.Y. and Tang, X.H. (2007) Oscillation of Solutions of Neutral Differential Equations with a Superlinear Neutral Term. Applied Mathematics Letters, 20, 1016-1022.
http://dx.doi.org/10.1016/j.aml.2006.11.006

[18]   Ruan, S.G. (1993) Oscillations of Second Order Neutral Differential Equations. Canadian Mathematical Bulletin, 36, 485-496.
http://dx.doi.org/10.4153/CMB-1993-064-4

[19]   Sahina, Y. (2004) On Oscillation of Second Order Neutral Type Delay Differential Equations. Applied Mathematics and Computation, 150, 697-706.
http://dx.doi.org/10.1016/S0096-3003(03)00300-X

[20]   Sun, S.R., Li, T.X., Han, Z.L. and Zhang, C. (2013) On Oscillation of Second Order Nonlinear Neutral Functional Differential Equations. Bulletin of the Malaysian Mathematical Sciences Society, 36, 541-554.

[21]   Xu, R. and Meng, F.W. (2007) Oscillation Crieria for Second Order Quasi-Linear Neutral Delay Differential Equations. Applied Mathematics and Computation, 192, 216-222.
http://dx.doi.org/10.1016/j.amc.2007.01.108

[22]   Ye, L.H. and Xu, Z.T. (2009) Oscillation Crieria for Second Order Quasilinear Neutral Delay Differential Equations. Applied Mathematics and Computation, 207, 388-396.
http://dx.doi.org/10.1016/j.amc.2008.10.051

[23]   Han, Z.L., Li, T.X., Sun, S.R. and Sun, Y.B. (2010) Remarks on the Paper [Appl. Math. Comput. 207(2009) 388-396]. Applied Mathematics and Computation, 215, 3998-4007.
http://dx.doi.org/10.1016/j.amc.2009.12.006

[24]   Arul, R. and Shobha, V.S. Oscillation of Second Order Neutral Differential Equations with Mixed Neutral Term. International Journal of Pure and Applied Mathematics. (To Appear)

 
 
Top