Abstract and Applied Analysis
Volume 2010 (2010), Article ID 278962, 19 pages
doi:10.1155/2010/278962
Research Article

Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument

Miroslav Bartušek,1 Mariella Cecchi,2 Zuzana Došlá,1 and Mauro Marini2

1Department of Mathematics and Statistics, Masaryk University, CZ-61137 Brno, Czech Republic
2Department of Electronic and Telecommunications, University of Florence, I-50139 Florence, Italy

Received 21 October 2009; Accepted 5 January 2010

Academic Editor: Paul Eloe

Copyright © 2010 Miroslav Bartušek 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. M. Bartušek, M. Cecchi, Z. Došlá, and M. Marini, “On nonoscillatory solutions of third order nonlinear differential equations,” Dynamic Systems and Applications, vol. 9, no. 4, pp. 483–499, 2000. View at Zentralblatt MATH · View at MathSciNet
  2. 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 · View at MathSciNet
  3. M. Cecchi, Z. Došlá, and M. Marini, “On third order differential equations with property A and B,” Journal of Mathematical Analysis and Applications, vol. 231, no. 2, pp. 509–525, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. M. Cecchi, Z. Došlá, and M. Marini, “Asymptotic behavior of solutions of third order delay differential equations,” Archivum Mathematicum, vol. 33, no. 1-2, pp. 99–108, 1997. View at Zentralblatt MATH · View at MathSciNet
  5. I. Mojsej, “Asymptotic properties of solutions of third-order nonlinear differential equations with deviating argument,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 11, pp. 3581–3591, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. H. Saker, “Oscillation criteria of third-order nonlinear delay differential equations,” Mathematica Slovaca, vol. 56, no. 4, pp. 433–450, 2006. View at Zentralblatt MATH · View at MathSciNet
  7. S. H. Saker, “Oscillation criteria of Hille and Nehari types for third-order delay differential equations,” Communications in Applied Analysis, vol. 11, no. 3-4, pp. 451–468, 2007. View at Zentralblatt MATH · View at MathSciNet
  8. S. R. Grace, R. P. Agarwal, R. Pavani, and E. Thandapani, “On the oscillation of certain third order nonlinear functional differential equations,” Applied Mathematics and Computation, vol. 202, no. 1, pp. 102–112, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. Tiryaki and M. F. Aktaş, “Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping,” Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 54–68, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. L. Erbe, “Oscillation, nonoscillation, and asymptotic behavior for third order nonlinear differential equations,” Annali di Matematica Pura ed Applicata, Series 4, vol. 110, pp. 373–391, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. W. Heidel, “Qualitative behavior of solutions of a third order nonlinear differential equation,” Pacific Journal of Mathematics, vol. 27, pp. 507–526, 1968. View at Zentralblatt MATH · View at MathSciNet
  12. Y. Feng, “Solution and positive solution of a semilinear third-order equation,” Journal of Applied Mathematics and Computing, vol. 29, no. 1-2, pp. 153–161, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. F. M. Minhós, “On some third order nonlinear boundary value problems: existence, location and multiplicity results,” Journal of Mathematical Analysis and Applications, vol. 339, no. 2, pp. 1342–1353, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. Bartušek, M. Cecchi, and M. Marini, “On Kneser solutions of nonlinear third order differential equations,” Journal of Mathematical Analysis and Applications, vol. 261, no. 1, pp. 72–84, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. P. K. Palamides and R. P. Agarwal, “An existence theorem for a singular third-order boundary value problem on [0,+∞),” Applied Mathematics Letters, vol. 21, no. 12, pp. 1254–1259, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  16. I. T. Kiguradze, “An oscillation criterion for a class of ordinary differential equations,” Differentsial'nye Uravneniya, vol. 28, no. 2, pp. 207–219, 1992. View at Zentralblatt MATH · View at MathSciNet
  17. O. Boruvka, Linear Differential Transformationen 2. Ordung, VEB, Berlin, Germany, 1967.
  18. M. Marini, “Criteri di limitatezza per le soluzioni dell'equazione lineare del secondo ordine,” Bollettino della Unione Matematica Italiana, vol. 4, pp. 225–231, 1971.
  19. P. Hartman, Ordinary Differential Equations, John Wiley & Sons, New York, NY, USA, 1964. View at MathSciNet
  20. E. F. Beckenbach and R. Bellman, Inequalities, vol. 30 of Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Springer, Berlin, Germany, 1961. View at MathSciNet