Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations

Yanxiang Shi; Di Liu

doi:doi:10.11648/j.pamj.20140305.11

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Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations

Yanxiang Shi, Di Liu

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 5)

Received: 28 August 2014 Accepted: 13 September 2014 Published: 20 September 2014

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Abstract

Oscillation criteria for a class of second order neutral delay differential equations of the form [c(t)((x(t)+p(t)x(t-τ))^' )^α ]^'+q(t)f(x(t-σ) )=0,t≥t_0 is studied. By using first and second mean value theorem of integrals, the new sufficient condition is obtained and the corresponding result what was already obtained is generalized by the result in this paper.

Published in	Pure and Applied Mathematics Journal (Volume 3, Issue 5)
DOI	10.11648/j.pamj.20140305.11
Page(s)	95-98
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), 2014. Published by Science Publishing Group

Keywords

Neutral Delay Differential Equation, Oscillatory Solution, Eventually Positive Solution

References

[1]	R.K. Zhang and W.T. Li, “Interval oscillation criteria for second order neutral nonlinear differential equations,” Applied Mathematics and Computation, vol. 157, 2004, pp. 39–51.
[2]	Q. Men and J.R. Yan, “Bounded oscillation for second order non-linear neutral delay differential equations in critical and non-critical case,” Nonlinear Analysis, vol. 64, 2006, pp. 1543-1561.
[3]	X.Y. Lin, “Oscillation of second-order nonlinear neutral differential equations,” Journal of Mathematical Analysis and Applications, vol. 309, 2005, pp. 442–454.
[4]	J.C. Jiang and X.P. Li, “Oscillation of second order nonlinear neutral differential equations,” Applied Mathematics and Computation, vol. 135, 2003, pp. 531–540.
[5]	M.M.A. ElSheikh and R. Sallam, “Oscillation criteria for second order functional differential equations,” Applied Mathematics and Computation, vol. 115, 2000, pp. 113-121.
[6]	Y. Sahiner, “On oscillation of second order neutral type delay differential equations,” Applied Mathematics and Computation, vol. 150, 2004, pp. 697-706.
[7]	S. James and W. Wong, “Necessary and sufficient conditions for oscillation of second order neutral differential equations,” Journal of Mathematical Analysis and Applications, vol.252, 2004, pp. 342-352.
[8]	Z.G. Ouyang, “Necessary and sufficient conditions for oscillation of odd order neutral delay parabolic differential equations,” Applied Mathematics and Computation, vol. 16, 2003, pp. 1039-1045.
[9]	H.J. Li and W.L. Liu, “Oscillation of second order neutral differential equations,” Mathematics Computation Modelling, vol. 1, 1995, pp. 45-53.
[10]	Y.X. Shi, “Oscillation criteria for nth order nonlinear neutral differential equations,” Applied Mathematics and Computation, vol. 235, 2014, pp. 423-429.

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Yanxiang Shi, Di Liu. (2014). Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations. Pure and Applied Mathematics Journal, 3(5), 95-98. https://doi.org/10.11648/j.pamj.20140305.11

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ACS Style

Yanxiang Shi; Di Liu. Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations. Pure Appl. Math. J. 2014, 3(5), 95-98. doi: 10.11648/j.pamj.20140305.11

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AMA Style

Yanxiang Shi, Di Liu. Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations. Pure Appl Math J. 2014;3(5):95-98. doi: 10.11648/j.pamj.20140305.11

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@article{10.11648/j.pamj.20140305.11,
  author = {Yanxiang Shi and Di Liu},
  title = {Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {5},
  pages = {95-98},
  doi = {10.11648/j.pamj.20140305.11},
  url = {https://doi.org/10.11648/j.pamj.20140305.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140305.11},
  abstract = {Oscillation criteria for a class of second order neutral delay differential equations of the form [c(t)((x(t)+p(t)x(t-τ))^' )^α ]^'+q(t)f(x(t-σ) )=0,t≥t_0 is studied. By using first and second mean value theorem of integrals, the new sufficient condition is obtained and the corresponding result what was already obtained is generalized by the result in this paper.},
 year = {2014}
}

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TY  - JOUR
T1  - Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations
AU  - Yanxiang Shi
AU  - Di Liu
Y1  - 2014/09/20
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20140305.11
DO  - 10.11648/j.pamj.20140305.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 95
EP  - 98
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20140305.11
AB  - Oscillation criteria for a class of second order neutral delay differential equations of the form [c(t)((x(t)+p(t)x(t-τ))^' )^α ]^'+q(t)f(x(t-σ) )=0,t≥t_0 is studied. By using first and second mean value theorem of integrals, the new sufficient condition is obtained and the corresponding result what was already obtained is generalized by the result in this paper.
VL  - 3
IS  - 5
ER  -

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Author Information

Yanxiang Shi

School of Mathematical Sciences, Shanxi University, Taiyuan, China
Di Liu

School of Mathematical Sciences, Shanxi University, Taiyuan, China

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APA Style

Yanxiang Shi, Di Liu. (2014). Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations. Pure and Applied Mathematics Journal, 3(5), 95-98. https://doi.org/10.11648/j.pamj.20140305.11

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ACS Style

Yanxiang Shi; Di Liu. Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations. Pure Appl. Math. J. 2014, 3(5), 95-98. doi: 10.11648/j.pamj.20140305.11

Copy | Download

AMA Style

Yanxiang Shi, Di Liu. Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations. Pure Appl Math J. 2014;3(5):95-98. doi: 10.11648/j.pamj.20140305.11

Copy | Download

@article{10.11648/j.pamj.20140305.11,
  author = {Yanxiang Shi and Di Liu},
  title = {Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {5},
  pages = {95-98},
  doi = {10.11648/j.pamj.20140305.11},
  url = {https://doi.org/10.11648/j.pamj.20140305.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140305.11},
  abstract = {Oscillation criteria for a class of second order neutral delay differential equations of the form [c(t)((x(t)+p(t)x(t-τ))^' )^α ]^'+q(t)f(x(t-σ) )=0,t≥t_0 is studied. By using first and second mean value theorem of integrals, the new sufficient condition is obtained and the corresponding result what was already obtained is generalized by the result in this paper.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations
AU  - Yanxiang Shi
AU  - Di Liu
Y1  - 2014/09/20
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20140305.11
DO  - 10.11648/j.pamj.20140305.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 95
EP  - 98
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20140305.11
AB  - Oscillation criteria for a class of second order neutral delay differential equations of the form [c(t)((x(t)+p(t)x(t-τ))^' )^α ]^'+q(t)f(x(t-σ) )=0,t≥t_0 is studied. By using first and second mean value theorem of integrals, the new sufficient condition is obtained and the corresponding result what was already obtained is generalized by the result in this paper.
VL  - 3
IS  - 5
ER  -

Copy | Download