Oscillations of Neutral Difference Equations of Second Order with Positive and Negative Coefficients

Hussain Ali Mohamad; Hala Majid Mohi

doi:doi:10.11648/j.pamj.20160501.12

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Oscillations of Neutral Difference Equations of Second Order with Positive and Negative Coefficients

Hussain Ali Mohamad, Hala Majid Mohi

Published in Pure and Applied Mathematics Journal (Volume 5, Issue 1)

Received: 19 November 2015 Accepted: 7 December 2015 Published: 29 January 2016

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Abstract

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 |y_n |→∞ as n→∞. Examples are given to illustrate the obtained results.

Published in	Pure and Applied Mathematics Journal (Volume 5, Issue 1)
DOI	10.11648/j.pamj.20160501.12
Page(s)	9-14
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Oscillation, Neutral Difference Equations, Second Order Difference Equations

References

[1]	S. N. Elaydi: An introduction to difference equations. Springer-Verlag New York, Inc., 2005.
[2]	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.
[3]	I. Gyori, G. Ladas: Oscillation theory of delay differential equations with applications. Oxford Clarendon Press, 1991.
[4]	Hasan ögunmez, Özkan Öcalan: Oscillations of difference equations with several positive and negative coefficients. Fasciculi mathematic, 51(2013), 115–122.
[5]	G. Ladas: Oscillations of difference equations with positive and negative coefficients, Rocky Mountain J. of Math., 20(4) (1990), 1051–1061.
[6]	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.
[7]	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.
[8]	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.
[9]	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.
[10]	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.
[11]	Zhiguo Luo, Jianhua Shen: New Oscillation Criteria for Delay Difference Equations. Journal of Mathematical Analysis and Applications, 264 (2001), 85–95.
[12]	W. R. Wade: An Introduction to Analysis. Third edition, Pearson Prentice Hall, 2004.

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APA Style

Hussain Ali Mohamad, Hala Majid Mohi. (2016). Oscillations of Neutral Difference Equations of Second Order with Positive and Negative Coefficients. Pure and Applied Mathematics Journal, 5(1), 9-14. https://doi.org/10.11648/j.pamj.20160501.12

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ACS Style

Hussain Ali Mohamad; Hala Majid Mohi. Oscillations of Neutral Difference Equations of Second Order with Positive and Negative Coefficients. Pure Appl. Math. J. 2016, 5(1), 9-14. doi: 10.11648/j.pamj.20160501.12

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AMA Style

Hussain Ali Mohamad, Hala Majid Mohi. Oscillations of Neutral Difference Equations of Second Order with Positive and Negative Coefficients. Pure Appl Math J. 2016;5(1):9-14. doi: 10.11648/j.pamj.20160501.12

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@article{10.11648/j.pamj.20160501.12,
  author = {Hussain Ali Mohamad and Hala Majid Mohi},
  title = {Oscillations of Neutral Difference Equations of Second Order with Positive and Negative Coefficients},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {1},
  pages = {9-14},
  doi = {10.11648/j.pamj.20160501.12},
  url = {https://doi.org/10.11648/j.pamj.20160501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160501.12},
  abstract = {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.},
 year = {2016}
}

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TY  - JOUR
T1  - Oscillations of Neutral Difference Equations of Second Order with Positive and Negative Coefficients
AU  - Hussain Ali Mohamad
AU  - Hala Majid Mohi
Y1  - 2016/01/29
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160501.12
DO  - 10.11648/j.pamj.20160501.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 9
EP  - 14
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160501.12
AB  - 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.
VL  - 5
IS  - 1
ER  -

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Author Information

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

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APA Style

Hussain Ali Mohamad, Hala Majid Mohi. (2016). Oscillations of Neutral Difference Equations of Second Order with Positive and Negative Coefficients. Pure and Applied Mathematics Journal, 5(1), 9-14. https://doi.org/10.11648/j.pamj.20160501.12

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ACS Style

Hussain Ali Mohamad; Hala Majid Mohi. Oscillations of Neutral Difference Equations of Second Order with Positive and Negative Coefficients. Pure Appl. Math. J. 2016, 5(1), 9-14. doi: 10.11648/j.pamj.20160501.12

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AMA Style

Hussain Ali Mohamad, Hala Majid Mohi. Oscillations of Neutral Difference Equations of Second Order with Positive and Negative Coefficients. Pure Appl Math J. 2016;5(1):9-14. doi: 10.11648/j.pamj.20160501.12

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@article{10.11648/j.pamj.20160501.12,
  author = {Hussain Ali Mohamad and Hala Majid Mohi},
  title = {Oscillations of Neutral Difference Equations of Second Order with Positive and Negative Coefficients},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {1},
  pages = {9-14},
  doi = {10.11648/j.pamj.20160501.12},
  url = {https://doi.org/10.11648/j.pamj.20160501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160501.12},
  abstract = {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.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Oscillations of Neutral Difference Equations of Second Order with Positive and Negative Coefficients
AU  - Hussain Ali Mohamad
AU  - Hala Majid Mohi
Y1  - 2016/01/29
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160501.12
DO  - 10.11648/j.pamj.20160501.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 9
EP  - 14
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160501.12
AB  - 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.
VL  - 5
IS  - 1
ER  -

Copy | Download