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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 395368, 11 pages
http://dx.doi.org/10.1155/2014/395368
Research Article

Asymptotic Behavior of Higher-Order Quasilinear Neutral Differential Equations

1Qingdao Technological University, Feixian, Shandong 273400, China
2Department of Mathematical Sciences, University of Agder, P.O. Box 422, 4604 Kristiansand, Norway

Received 29 September 2013; Accepted 17 November 2013; Published 19 January 2014

Academic Editor: Josef Diblik

Copyright © 2014 Tongxing Li and Yuriy V. Rogovchenko. 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. C. H. Ou and J. S. W. Wong, “Oscillation and non-oscillation theorems for superlinear Emden-Fowler equations of the fourth order,” Annali di Matematica Pura ed Applicata. Series IV, vol. 183, no. 1, pp. 25–43, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. S. W. Wong, “On the generalized Emden-Fowler equation,” SIAM Review, vol. 17, pp. 339–360, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. R. P. Agarwal, L. Berezansky, E. Braverman, and A. Domoshnitsky, Nonoscillation Theory of Functional Differential Equations with Applications, Springer, New York, NY, USA, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  4. R. P. Agarwal, M. Bohner, and W.-T. Li, Nonoscillation and Oscillation: Theory for Functional Differential Equations, vol. 267, Marcel Dekker, New York, NY, USA, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  5. R. P. Agarwal, S. R. Grace, and D. O'Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic, Dordrecht, The Netherlands, 2000. View at MathSciNet
  6. 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
  7. B. Baculíková, “Properties of third-order nonlinear functional differential equations with mixed arguments,” Abstract and Applied Analysis, vol. 2011, Article ID 857860, 15 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. B. Baculíková and J. Džurina, “Oscillation theorems for second order neutral differential equations,” Computers & Mathematics with Applications, vol. 61, no. 1, pp. 94–99, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. B. Baculíková and J. Džurina, “Oscillation theorems for second-order nonlinear neutral differential equations,” Computers & Mathematics with Applications, vol. 62, no. 12, pp. 4472–4478, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. B. Baculíková and J. Džurina, “Oscillation theorems for higher order neutral differential equations,” Applied Mathematics and Computation, vol. 219, no. 8, pp. 3769–3778, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  11. B. Baculíková, J. Džurina, and T. Li, “Oscillation results for even-order quasilinear neutral functional differential equations,” Electronic Journal of Differential Equations, no. 143, pp. 1–9, 2011. View at Zentralblatt MATH · View at MathSciNet
  12. J. Džurina and B. Baculíková, “Oscillation and asymptotic behavior of higher-order nonlinear differential equations,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, Article ID 951898, 9 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. M. Hasanbulli and Yu. V. Rogovchenko, “Asymptotic behavior of nonoscillatory solutions to n-th order nonlinear neutral differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 4, pp. 1208–1218, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  14. M. Hasanbulli and Yu. V. Rogovchenko, “Oscillation criteria for second order nonlinear neutral differential equations,” Applied Mathematics and Computation, vol. 215, no. 12, pp. 4392–4399, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Y. Kitamura and T. Kusano, “Oscillation of first-order nonlinear differential equations with deviating arguments,” Proceedings of the American Mathematical Society, vol. 78, no. 1, pp. 64–68, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. T. Li, R. P. Agarwal, and M. Bohner, “Some oscillation results for second-order neutral differential equations,” The Journal of the Indian Mathematical Society, vol. 79, no. 1-4, pp. 97–106, 2012. View at Zentralblatt MATH · View at MathSciNet
  17. 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, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. T. Li, Yu. V. Rogovchenko, and C. Zhang, “Oscillation of second-order neutral differential equations,” Funkcialaj Ekvacioj, vol. 56, no. 1, pp. 111–120, 2013. View at Zentralblatt MATH · View at MathSciNet
  19. T. Li and E. Thandapani, “Oscillation of solutions to odd-order nonlinear neutral functional differential equations,” Electronic Journal of Differential Equations, no. 23, pp. 1–12, 2011. View at Zentralblatt MATH · View at MathSciNet
  20. Ch. G. Philos, “A new criterion for the oscillatory and asymptotic behavior of delay differential equations,” Bulletin de l'Académie Polonaise des Sciences, vol. 39, pp. 61–64, 1981.
  21. Ch. G. Philos, “On the existence of nonoscillatory solutions tending to zero at for differential equations with positive delays,” Archiv der Mathematik, vol. 36, no. 2, pp. 168–178, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. G. Xing, T. Li, and C. Zhang, “Oscillation of higher-order quasi-linear neutral differential equations,” Advances in Difference Equations, vol. 2011, article 45, p. 10, 2011. View at Zentralblatt MATH · 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 Zentralblatt MATH · View at MathSciNet
  24. C. Zhang, T. Li, R. P. Agarwal, and M. Bohner, “Oscillation results for fourth-order nonlinear dynamic equations,” Applied Mathematics Letters, vol. 25, no. 12, pp. 2058–2065, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. 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 Zentralblatt MATH · View at MathSciNet