About this Journal Submit a Manuscript Table of Contents
International Journal of Differential Equations
Volume 2014 (2014), Article ID 437278, 5 pages
http://dx.doi.org/10.1155/2014/437278
Research Article

Oscillation Criteria for Certain Even Order Neutral Delay Differential Equations

Department of Applied Mathematics, Palestine Polytechnic University, Hebron, Palestine

Received 20 January 2014; Accepted 1 April 2014; Published 16 April 2014

Academic Editor: Yuriy Rogovchenko

Copyright © 2014 Ruba Al-Hamouri and Ali Zein. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Hale, Theory of Functional Differential Equations, Springer, New York, NY, USA, 2nd edition, 1977. View at MathSciNet
  2. R. P. Agarwal, S. R. Grace, and D. O'Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000. View at MathSciNet
  3. J. Džurina, “Oscillation theorems for second order advanced neutral differential equations,” Tatra Mountains Mathematical Publications, vol. 48, pp. 61–71, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. L. Erbe, T. S. Hassan, and A. Peterson, “Oscillation of second order neutral delay differential equations,” Advances in Dynamical Systems and Applications, vol. 3, no. 1, pp. 53–71, 2008. View at MathSciNet
  5. S. R. Grace and B. S. Lalli, “Oscillation of nonlinear second order neutral differential equations,” Rationalisation (Mathematics), vol. 3, pp. 77–84, 1987.
  6. M. K. Grammatikopoulos, G. Ladas, and A. Meimaridou, “Oscillations of second order neutral delay differential equations,” Radovi Matematički, vol. 1, no. 2, pp. 267–274, 1985. View at Zentralblatt MATH · View at MathSciNet
  7. G. S. Ladde, V. Lakshmikantham, and B. G. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, vol. 110, Marcel Dekker, New York, NY, USA, 1987. View at MathSciNet
  8. T. Li, B. Baculíková, and J. Džurina, “Oscillation results for second-order neutral differential equations of mixed type,” Tatra Mountains Mathematical Publications, vol. 48, pp. 101–116, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. T. Li, Z. Han, P. Zhao, and S. Sun, “Oscillation of even-order neutral delay differential equations,” Advances in Difference Equations, vol. 2010, Article ID 184180, 9 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. T. Li and Y. V. Rogovchenko, “Asymptotic behavior of higher-order quasilinear neutral differential equations,” Abstract and Applied Analysis, vol. 2014, Article ID 395368, 11 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  11. F. Meng and R. Xu, “Oscillation criteria for certain even order quasi-linear neutral differential equations with deviating arguments,” Applied Mathematics and Computation, vol. 190, no. 1, pp. 458–464, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. C. Philos, “A new criterion for the oscillatory and asymptotic behavior of delay differential equations,” L'Académie Polonaise des Sciences. Bulletin, vol. 29, no. 7-8, pp. 367–370, 1981. View at Zentralblatt MATH · View at MathSciNet
  13. Y. Sun, Z. Han, S. Sun, and C. Zhang, “Oscillation criteria for even order nonlinear neutral differential equations,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 30, pp. 1–12, 2012. View at MathSciNet
  14. G. Xing, T. Li, and C. Zhang, “Oscillation of higher-order quasi-linear neutral differential equations,” Advances in Difference Equations, vol. 2011, article 45, 2011. View at Zentralblatt MATH · View at MathSciNet
  15. A. Zafer, “Oscillation criteria for even order neutral differential equations,” Applied Mathematics Letters, vol. 11, no. 3, pp. 21–25, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. A. Zafer and R. S. Dahiya, “Oscillation of bounded solutions of neutral differential equations,” Applied Mathematics Letters, vol. 6, no. 2, pp. 43–46, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet