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

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.
Cite This Article
  • 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

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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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    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
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    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.
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    IS  - 5
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Author Information
  • School of Mathematical Sciences, Shanxi University, Taiyuan, China

  • School of Mathematical Sciences, Shanxi University, Taiyuan, China

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