Oscillations of Neutral Difference Equations of Second Order with Positive and Negative Coefficients
Pure and Applied Mathematics Journal
Volume 5, Issue 1, February 2016, Pages: 9-14
Received: Nov. 19, 2015;
Accepted: Dec. 7, 2015;
Published: Jan. 29, 2016
Views 3998 Downloads 165
Hussain Ali Mohamad, Dept. of Mathematics, College of Science for Women, University of Baghdad, Baghdad, Iraq
Hala Majid Mohi, Dept. of Mathematics, College of Science for Women, University of Baghdad, Baghdad, Iraq
In this paper some necessary and sufficient conditions are obtained to guarantee the oscillation for bounded and all solutions of second order nonlinear neutral delay difference equations. In Theorem 5 and Theorem 8, We have studied the oscillation criteria as well as the asymptotic behavior, where was established some sufficient conditions to ensure that every solution are either oscillates or |yn |→∞ as n→∞. Examples are given to illustrate the obtained results.
Hussain Ali Mohamad,
Hala Majid Mohi,
Oscillations of Neutral Difference Equations of Second Order with Positive and Negative Coefficients, Pure and Applied Mathematics Journal.
Vol. 5, No. 1,
2016, pp. 9-14.
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
S. N. Elaydi: An introduction to difference equations. Springer-Verlag New York, Inc., 2005.
E. George Chatzarakis, G. Christos Philos, P. Ioannis Stavroulakis: On the oscillation of solutions to linear difference equation with variable delay, Electronic Journal of Differential Equations, Vol. (2008), No. 50, 1–15.
I. Gyori, G. Ladas: Oscillation theory of delay differential equations with applications. Oxford Clarendon Press, 1991.
Hasan ögunmez, Özkan Öcalan: Oscillations of difference equations with several positive and negative coefficients. Fasciculi mathematic, 51(2013), 115–122.
G. Ladas: Oscillations of difference equations with positive and negative coefficients, Rocky Mountain J. of Math., 20(4) (1990), 1051–1061.
R. N. Rath, L. N. Padhy: Necessary and sufficient conditions for oscillations of solutions of a first order forced nonlinear difference equation with several delays. Fasc. Math., 35(2005), 99–113.
R. N. Rath, L. N. Padhy: Oscillations and non-oscillations of neutral difference equations of first order with positive and negative coefficients. Fasc. Math., 37(2007), 57–65.
X. H. Tang, J. S. Yu, D. H. Peng: Oscillations and non- oscillations of neutral difference equations with positive and negative coefficients. Computers and mathematics application, 39 (2000), 169–181.
A. K. Tripathy, S. Panigrahi: Oscillations in nonlinear neutral difference equation with positive and negative coefficients: International Journal of Difference Equations. Vol. 5, No. 2, (2010), 251–265.
Xiaohui Gong, Xiaozhu Zhong, Jianqiang Jia, Rui Ouyang, Hongqiang Han: Oscillations of first order neutral difference equations. Modern Applied science, Vol. 3, No. 8, (2009), 90–94.
Zhiguo Luo, Jianhua Shen: New Oscillation Criteria for Delay Difference Equations. Journal of Mathematical Analysis and Applications, 264 (2001), 85–95.
W. R. Wade: An Introduction to Analysis. Third edition, Pearson Prentice Hall, 2004.