WSEAS Transactions on Mathematics


Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 17, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 17, 2018



On the Oscillatory Behavior of Solutions of Second Order Nonlinear Neutral Delay Differential Equations

AUTHORS: M. M. A. El-Sheikh, R. A. Sallam, E. I. El-Saedy

Download as PDF

ABSTRACT: In this paper, the oscillatory behavior of solutions of a general class of nonlinear neutral delay differential equations is discussed. New criteria are established. Illustrative examples are also given to support the validity of the method

KEYWORDS: Oscillation, Second order, Non-linear neutral delay differential equations

REFERENCES:

[1] R. Arul and V. S. Shobha, Improvement results for oscillatory behavior of second order neutral differential equations with nonpositive neutral term, British Journal of Mathematics and Computer Science, Vol.12, No.5, 2016, pp. 1-7.

[2] B. Baculíková and J. Džurina, Oscillation of third-order neutral differential equations, Mathematical and Computer Modelling, Vol. 52, 2010, pp. 215-226.

[3] B. Baculíková and J. Džurina, Oscillation theorems for second order neutral differential equations, Computers and Mathematics with Applications,Vol. 61, No. 1, 2011, pp. 94-99.

[4] B. Baculíková and J. Džurina, Oscillation theorems for second order nonlinear neutral differential equations, Computers and Mathematics with Applications, Vol. 62, No. 12, 2011, pp. 4472-4478.

[5] J. Džurina, Ethiraju Thandapani, and Sivaraj Tamilvanan, Oscillation of solutions to thirdorder half-linear neutral differential equations, Electronic Journal of Differential Equations, Vol. 2012, No. 29, 2012, pp. 1-9.

[6] M. M. A. El-Sheikh, Oscillation and nonoscillation criteria for second order nonlinear differential equations, J. Mathematical Analysis and Application, Vol. 179, No. 1, 1993, pp. 14-27.

[7] M. M. A. El-Sheikh, R. Sallam, D. Elimy, Oscillation criteria for second order nonlinear equations with damping, Advances in Differential Equations and Control Process ,Vol. 8, No. 2, 2011, pp. 127-142.

[8] M. M. A. El-Sheikh, R. Sallam and N. Mohamady, Oscillation criteria for second order nonlinear neutral differential equations, Differential Equations and Control Processes, No.3, 2011.

[9] L. Erbe, T. S. Hassan and A. Peterson, Oscillation of second order neutral delay differential equations, Advances in Dynamical Systems and Applications, Vol. 3, No.1, 2008, pp. 53-71.

[10] J. K. Hale, Theory of functional differential equation, Springer-Verlag, New York, 1977.

[11] Z. Han, T. Li, S. Sun and W. Chen, Oscillation of second order quasilinear neutral delay differential equations, J. Appl. Math. Comput., Vol. 40, 2012, pp. 143-152.

[12] M. Hassanbulli and Yu. V. Rogovchenko, Oscillation criteria for second order nonlinear neutral differential equations, Applied Mathematics and Computation, Vol. 215, No. 12, 2010, pp. 4392-4399.

[13] T. Li, Yu. V. Rogovchenco, and C. Zhang, Oscillation results for second order nonlinear neutral differential equations, Advances in Difference Equations, Vol. 2013, 2013, pp. 1- 13.

[14] T. Li and Yu. V. Rogovchenco, Oscillation theorems for second order nonlinear neutral delay differential equations, Abstract and Applied Analysis, Vol. 2014, 2014, 5 pages.

[15] T. Li and Yu. V. Rogovchenko, Oscillatory behavior of second order nonlinear neutral differential equations, Hindawi Publishing Corporation Abstract and Applied Analysis, Vol. 2014, 2014, 8 pages.

[16] Qi Li, Rui Wang, Feng Chen and Tongxing Li, Oscillation of second order nonlinear delay differential equations with nonpositive neutral coefficients, Advance in Difference Equations, Vol. 2015, 2015, 7 pages.

[17] H. A. Mohamad, I. Z. Mushtt, Oscillation of second order nonlinear neutral differential equations, Pure and Applied Mathematics Journal, Vol. 4, No. 2, 2015, pp. 62-65.

[18] R. N. Rath, L. N. Padhy, N. Misra, Oscillation of solutions of non-linear neutral delay differential equations of higher order for p(t)=±1, Archivum Mathematicum (Brno), Vol. 40, 2004, pp. 359-336.

[19] A. A. Soliman, R. A. Sallam, A. M. Hassan, Oscillation criteria of second order nonlinear neutal differential equations, International Journal of Applied Mathematical Research, Vol. 1, No. 3, 2012, pp. 314-322.

[20] A. A. Soliman, R. A. Sallam, A. Elbitar, A. M. Hassan, Oscillation criteria of third order nonlinear neutral differential equations, International Journal of Applied Mathematiclal Research, Vol. 1, No. 3, 2012, pp. 268-281.

[21] Y. G. Sun, F. W. Meng, Note on the paper of Džurina and Stavroulakis, Appl. Math. Comput., Vol. 174, 2006, pp. 1634-1641.

[22] J. S. W. Wong, Necessary and sufficient conditions for oscillation of second order neutral differential equations, Journal of Mathematical Analysis and Applications,Vol. 252, 2000, pp. 342-352.

[23] M. K. Yildiz, Basak Karpuz, Özkan Öcalan, Oscillation of nonlinear neutral delay differential equations of second-order with nonpositive and negative coefficients,Turk J Math, Vol. 33, 2009, pp. 341-350.

[24] S. Y. Zhang, Qi-Ru Wang, Oscillation of second order nonlinear neutral dynamic equations on time scales, Applied Mathematics and Computation, Vol. 216, 2010, pp. 2837- 2848.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #8, pp. 51-57


Copyright © 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

Bulletin Board

Currently:

The editorial board is accepting papers.


WSEAS Main Site