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Abstract and Applied Analysis
Volume 2014, Article ID 629074, 11 pages
http://dx.doi.org/10.1155/2014/629074
Research Article

Oscillation Criteria for Certain Even Order Neutral Delay Differential Equations with Mixed Nonlinearities

School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China

Received 16 March 2014; Accepted 21 June 2014; Published 3 August 2014

Academic Editor: Tongxing Li

Copyright © 2014 Zhen-Lai Han et al. 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. R. P. Agarwal, S. R. Grace, and D. O'Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic, Dordrecht, The Netherlands, 2000.
  2. R. P. Agarwal, S. R. Grace, and D. O'Regan, “Oscillation criteria for certain nth order differential equations with deviating arguments,” Journal of Mathematical Analysis and Applications, vol. 262, no. 2, pp. 601–622, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. R. P. Agarwal and S. R. Grace, “Oscillation theorems for certain functional differential equations of higher order,” Mathematical and Computer Modelling, vol. 39, no. 9-10, pp. 1185–1194, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. Y. Sun and F. Meng, “Note on the paper of Džurina and Stavroulakis,” Applied Mathematics and Computation, vol. 174, pp. 1634–1641, 2006. View at Google Scholar
  5. C. H. G. Philos, “A new criteria for the oscillatory and asymptotic behavior of delay differential equations,” Bulletin of the Polish Academy of Sciences Mathematics, vol. 39, pp. 61–64, 1981. View at Google Scholar
  6. Y. G. Sun and F. W. Meng, “Oscillation of second-order delay differential equations with mixed nonlinearities,” Applied Mathematics and Computation, vol. 207, no. 1, pp. 135–139, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. Z. Xu and Y. Xia, “Integral averaging technique and oscillation of certain even order delay differential equations,” Journal of Mathematical Analysis and Applications, vol. 292, no. 1, pp. 238–246, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. C. Zhang, T. Li, B. Sun, and E. Thandapani, “On the oscillation of higher-order half-linear delay differential equations,” Applied Mathematics Letters, vol. 24, no. 9, pp. 1618–1621, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Z. Han, T. Li, S. Sun, and Y. Sun, “Remarks on the paper [Appl. Math. Comput. 207 (2009) 388–396],” Applied Mathematics and Computation, vol. 215, no. 11, pp. 3998–4007, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. R. Xu and F. Meng, “New Kamenev-type oscillation criteria for second order neutral nonlinear differential equations,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1364–1370, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. B. Karpuz, J. V. Manojlović, Ö. Öcalan, and Y. Shoukaku, “Oscillation criteria for a class of second-order neutral delay differential equations,” Applied Mathematics and Computation, vol. 210, no. 2, pp. 303–312, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. L. H. Liu and Y. Z. Bai, “New oscillation criteria for second-order nonlinear neutral delay differential equations,” Journal of Computational and Applied Mathematics, vol. 231, no. 2, pp. 657–663, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. Z. Han, T. Li, S. Sun, and W. Chen, “Oscillation criteria for second-order nonlinear neutral delay differential equations,” Advances in Difference Equations, vol. 2010, Article ID 763278, 23 pages, 2010. View at Publisher · View at Google Scholar
  14. T. Li, Z. Han, C. Zhang, and S. Sun, “On the oscillation of second-order Emden-Fowler neutral differential equations,” Journal of Applied Mathematics and Computing, vol. 37, no. 1-2, pp. 601–610, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  15. Z. Han, T. Li, C. Zhang, and Y. Sun, “Oscillation criteria for certain second-order nonlinear neutral differential equations of mixed type,” Abstract and Applied Analysis, vol. 2011, Article ID 387483, 9 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. S. Sun, T. Li, Z. Han, and Y. Sun, “Oscillation of second-order neutral functional differential equations with mixed nonlinearities,” Abstract and Applied Analysis, vol. 2011, Article ID 927690, 15 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. Z. Han, T. Li, S. Sun, and W. Chen, “Oscillation criteria for second-order nonlinear neutral delay differential equations,” Advances in Difference Equations, vol. 2010, Article ID 763278, 8 pages, 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. T. Li, Z. Han, C. Zhang, and H. Li, “Oscillation criteria for second-order superlinear neutral differential equations,” Abstract and Applied Analysis, vol. 2011, Article ID 367541, 17 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. 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 MathSciNet · View at Scopus
  20. 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 MathSciNet
  21. Y. Sun and Z. Han, “Oscillation criteria for even order half-linear neutral delay differential equations with damping,” in Proceedings of the 5th International Congress on Mathematical Biology (ICMB '11), vol. 1, pp. 120–124, World Academic Press, Nanjing, China, 2011.
  22. 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. 2012, no. 30, pp. 1–12, 2012. View at Google Scholar · View at MathSciNet
  23. C. Zhang, R. P. Agarwal, M. Bohner, and T. Li, “New results for oscillatory behavior of even-order half-linear delay differential equations,” Applied Mathematics Letters, vol. 26, no. 2, pp. 179–183, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. R. P. Agarwal, M. Bohner, and T. Li, “A new approach in the study of oscillatory behavior of even-order neutral delay differential equations,” Applied Mathematics and Computation, vol. 225, pp. 787–794, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  25. C. Zhang, R. P. Agarwal, and T. Li, “Oscillation and asymptotic behavior of higher-order delay differential equations with p-Laplacian like operators,” Journal of Mathematical Analysis and Applications, vol. 409, no. 2, pp. 1093–1106, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus