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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 730128, 10 pages
http://dx.doi.org/10.1155/2011/730128
Research Article

Asymptotic Properties of Third-Order Delay Trinomial Differential Equations

Department of Mathematics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 042 00 Košice, Slovakia

Received 2 September 2010; Accepted 3 November 2010

Academic Editor: Yuri Rogovchenko

Copyright © 2011 J. Džurina and R. Komariková. 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. B. Baculíková, E. M. Elabbasy, S. H. Saker, and J. Džurina, “Oscillation criteria for third-order nonlinear differential equations,” Mathematica Slovaca, vol. 58, no. 2, pp. 201–220, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. B. Baculíková, “Oscillation criteria for second order nonlinear differential equations,” Archivum Mathematicum, vol. 42, no. 2, pp. 141–149, 2006. View at Zentralblatt MATH
  3. B. Baculíková, “Oscillation of certain class of the third order neutral differential equations,” Abstract and Applied Analysis. In press.
  4. B. Baculíková and D. Lacková, “Oscillation criteria for second order retarded differential equations,” Studies of the University of Žilina. Mathematical Series, vol. 20, no. 1, pp. 11–18, 2006.
  5. M. Bartušek, M. Cecchi, Z. Došlá, and M. Marini, “Oscillation for third-order nonlinear differential equations with deviating argument,” Abstract and Applied Analysis, vol. 2010, Article ID 278962, 19 pages, 2010. View at Zentralblatt MATH
  6. R. Bellman, Stability Theory of Differential Equations, McGraw-Hill, New York, NY, USA, 1953.
  7. T. A. Chanturija and I. T. Kiguradze, Asymptotic Properties of Nonautonomous Ordinary Differential Equations, Nauka, Moscow, Russia, 1990.
  8. J. Džurina, “Asymptotic properties of the third order delay differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 26, no. 1, pp. 33–39, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. J. Džurina, “Comparison theorems for nonlinear ODEs,” Mathematica Slovaca, vol. 42, no. 3, pp. 299–315, 1992.
  10. J. Džurina and R. Kotorová, “Properties of the third order trinomial differential equations with delay argument,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 5-6, pp. 1995–2002, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. L. Erbe, “Existence of oscillatory solutions and asymptotic behavior for a class of third order linear differential equations,” Pacific Journal of Mathematics, vol. 64, no. 2, pp. 369–385, 1976. View at Zentralblatt MATH
  12. P. Hartman, Ordinary Differential Equations, John Wiley & Sons, New York, NY, USA, 1964.
  13. G. D. Jones, “An asymptotic property of solutions of y′′′+p(x)y+q(x)y=0,” Pacific Journal of Mathematics, vol. 47, pp. 135–138, 1973. View at Zentralblatt MATH
  14. T. Kusano and M. Naito, “Comparison theorems for functional-differential equations with deviating arguments,” Journal of the Mathematical Society of Japan, vol. 33, no. 3, pp. 509–532, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. T. Kusano, M. Naito, and K. Tanaka, “Oscillatory and asymptotic behaviour of solutions of a class of linear ordinary differential equations,” Proceedings of the Royal Society of Edinburgh A, vol. 90, no. 1-2, pp. 25–40, 1981. View at Zentralblatt MATH
  16. A. C. Lazer, “The behavior of solutions of the differential equation y′′′+p(x)y+q(x)y=0,” Pacific Journal of Mathematics, vol. 17, pp. 435–466, 1966. View at Zentralblatt MATH
  17. W. E. Mahfoud, “Comparison theorems for delay differential equations,” Pacific Journal of Mathematics, vol. 83, no. 1, pp. 187–197, 1979. View at Zentralblatt MATH
  18. N. Parhi and S. Padhi, “On asymptotic behavior of delay-differential equations of third order,” Nonlinear Analysis: Theory, Methods & Applications, vol. 34, no. 3, pp. 391–403, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. N. Parhi and S. Padhi, “Asymptotic behaviour of solutions of third order delay-differential equations,” Indian Journal of Pure and Applied Mathematics, vol. 33, no. 10, pp. 1609–1620, 2002. View at Zentralblatt MATH
  20. A. Škerlík, “Integral criteria of oscillation for a third order linear differential equation,” Mathematica Slovaca, vol. 45, no. 4, pp. 403–412, 1995. View at Zentralblatt MATH
  21. K. Tanaka, “Asymptotic analysis of odd order ordinary differential equations,” Hiroshima Mathematical Journal, vol. 10, no. 2, pp. 391–408, 1980. View at Zentralblatt MATH
  22. W. F. Trench, “Canonical forms and principal systems for general disconjugate equations,” Transactions of the American Mathematical Society, vol. 189, pp. 319–327, 1973.