Oscillation of Second Order Nonlinear Neutral Differential Equations

Hussain Ali Mohamad; Intidhar Zamil Mushtt

doi:doi:10.11648/j.pamj.20150402.16

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Oscillation of Second Order Nonlinear Neutral Differential Equations

Hussain Ali Mohamad, Intidhar Zamil Mushtt

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 2)

Received: 7 March 2015 Accepted: 24 March 2015 Published: 31 March 2015

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Abstract

The oscillation criteria are investigated for all solutions of second order nonlinear neutral delay differential equations. Our results extend and improve some results well known in the literature see ( [14] theorem 3.2.1 and theorem 3.2.2 pp.385-388). Some examples are given to illustrate our main results.

Published in	Pure and Applied Mathematics Journal (Volume 4, Issue 2)
DOI	10.11648/j.pamj.20150402.16
Page(s)	62-65
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), 2015. Published by Science Publishing Group

Keywords

Oscillation, Neutral Differential Equations

References

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[2]	R. Al-Hamouri and A. Zein: Oscillation Criteria for Certain even order neutral Delay Differential Equations, international Journal of Differential Equations, Vol 2014, Article ID 437278,5 pages.
[3]	B. Baculikov_a, J. D_zurina; Oscillation criteria for second order neutral differential equations. Mathematica Bohemica, 125 (2000) 2 145-153.
[4]	J. G. Dix Oscillation of solutions to a neutral di_erential equation involving an n-order operator with variable coefficients and a forcing term.. Differ. Equ. Dyn. Syst., 22 (2014),15{31.
[5]	M. Hasanbulli, Yu. V. Rogovchenko; Oscillation criteria for second order nonlinear neutral differential equations. Appl. Math. Comput., 215 (2010) 4392-4399.
[6]	B. Karpuz, Ö. Öcalan, S. Özturk; Comparison theorems on the oscillation and asymptotic behaviour of higher-order neutral differential equations. Glasgow Math. J., 52 (2010) 107-114.
[7]	G.S. Ladde, V. Lakshmikantham, B.G. Zhang : Oscillation Theory of Differential Equations with deviating Arguments Marcel Dekker inc, New York and Basel.,(1987).
[8]	Tongxing Li, Blanka Baculkov and Jozef Durina; Oscillatory behavior of second-order nonlinear neutral differential equations with distributed deviating arguments. Boundary value problem, 2014 (2014) 68 1-15.
[9]	T. Li; Comparison theorems for second-order neutral differential equations of mixed type. Electro. J. Diff. Equ., 2010 (2010) no. 167, 1-7.
[10]	T. Li, R. P. Agarwal, M. Bohner; Some oscillation results for second-order neutral differential equations. J. Indian Math. Soc., 79 (2012) 97-106.
[11]	L. Li, F. Meng; New results on Oscillation for even order neutral differential equations with deviating arguments. Advance Pure Mathematic, 1 (2011) 49-53.
[12]	T. Li, Z. Han, P. Zhao and S. Sun; Oscillation of even order differential equations. Advance in Difference Equations, 2010 (2010) 1-9.
[13]	R. N. Rath, L. N. Padhy and N. Misra; Oscillation of solution of nonlinear neutral delay differential equations of higher order for p(t)=±1. Archivum Mathematicum 40 (2004)359-366.
[14]	Samir Saker; Oscillation Theory of delay differential and di_erence equations of second order. VDM Verlag Dr. Muller, 2010.
[15]	M. K. Yildiz; Oscillation results of higher order nonlinear neutral delay differential equations with oscillating coefficients. Advance in Dynamical system and application, Vol3 No2 (2008)297-303.

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APA Style

Hussain Ali Mohamad, Intidhar Zamil Mushtt. (2015). Oscillation of Second Order Nonlinear Neutral Differential Equations. Pure and Applied Mathematics Journal, 4(2), 62-65. https://doi.org/10.11648/j.pamj.20150402.16

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ACS Style

Hussain Ali Mohamad; Intidhar Zamil Mushtt. Oscillation of Second Order Nonlinear Neutral Differential Equations. Pure Appl. Math. J. 2015, 4(2), 62-65. doi: 10.11648/j.pamj.20150402.16

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AMA Style

Hussain Ali Mohamad, Intidhar Zamil Mushtt. Oscillation of Second Order Nonlinear Neutral Differential Equations. Pure Appl Math J. 2015;4(2):62-65. doi: 10.11648/j.pamj.20150402.16

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@article{10.11648/j.pamj.20150402.16,
  author = {Hussain Ali Mohamad and Intidhar Zamil Mushtt},
  title = {Oscillation of Second Order Nonlinear Neutral Differential Equations},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {2},
  pages = {62-65},
  doi = {10.11648/j.pamj.20150402.16},
  url = {https://doi.org/10.11648/j.pamj.20150402.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150402.16},
  abstract = {The oscillation criteria are investigated for all solutions of second order nonlinear neutral delay differential equations. Our results extend and improve some results well known in the literature see ( [14] theorem 3.2.1 and theorem 3.2.2 pp.385-388). Some examples are given to illustrate our main results.},
 year = {2015}
}

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TY  - JOUR
T1  - Oscillation of Second Order Nonlinear Neutral Differential Equations
AU  - Hussain Ali Mohamad
AU  - Intidhar Zamil Mushtt
Y1  - 2015/03/31
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150402.16
DO  - 10.11648/j.pamj.20150402.16
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 62
EP  - 65
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150402.16
AB  - The oscillation criteria are investigated for all solutions of second order nonlinear neutral delay differential equations. Our results extend and improve some results well known in the literature see ( [14] theorem 3.2.1 and theorem 3.2.2 pp.385-388). Some examples are given to illustrate our main results.
VL  - 4
IS  - 2
ER  -

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Author Information

Hussain Ali Mohamad

University of Baghdad, College of Science for Women, Baghdad, Iraq
Intidhar Zamil Mushtt

Al Mustansiriyah University, College of Education, Baghdad, Iraq

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Plain Text BibTeX RIS

APA Style

Hussain Ali Mohamad, Intidhar Zamil Mushtt. (2015). Oscillation of Second Order Nonlinear Neutral Differential Equations. Pure and Applied Mathematics Journal, 4(2), 62-65. https://doi.org/10.11648/j.pamj.20150402.16

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ACS Style

Hussain Ali Mohamad; Intidhar Zamil Mushtt. Oscillation of Second Order Nonlinear Neutral Differential Equations. Pure Appl. Math. J. 2015, 4(2), 62-65. doi: 10.11648/j.pamj.20150402.16

Copy | Download

AMA Style

Hussain Ali Mohamad, Intidhar Zamil Mushtt. Oscillation of Second Order Nonlinear Neutral Differential Equations. Pure Appl Math J. 2015;4(2):62-65. doi: 10.11648/j.pamj.20150402.16

Copy | Download

@article{10.11648/j.pamj.20150402.16,
  author = {Hussain Ali Mohamad and Intidhar Zamil Mushtt},
  title = {Oscillation of Second Order Nonlinear Neutral Differential Equations},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {2},
  pages = {62-65},
  doi = {10.11648/j.pamj.20150402.16},
  url = {https://doi.org/10.11648/j.pamj.20150402.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150402.16},
  abstract = {The oscillation criteria are investigated for all solutions of second order nonlinear neutral delay differential equations. Our results extend and improve some results well known in the literature see ( [14] theorem 3.2.1 and theorem 3.2.2 pp.385-388). Some examples are given to illustrate our main results.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Oscillation of Second Order Nonlinear Neutral Differential Equations
AU  - Hussain Ali Mohamad
AU  - Intidhar Zamil Mushtt
Y1  - 2015/03/31
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150402.16
DO  - 10.11648/j.pamj.20150402.16
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 62
EP  - 65
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150402.16
AB  - The oscillation criteria are investigated for all solutions of second order nonlinear neutral delay differential equations. Our results extend and improve some results well known in the literature see ( [14] theorem 3.2.1 and theorem 3.2.2 pp.385-388). Some examples are given to illustrate our main results.
VL  - 4
IS  - 2
ER  -

Copy | Download