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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 498073, 18 pages
http://dx.doi.org/10.1155/2012/498073
Research Article

Oscillation Criteria of Certain Third-Order Differential Equation with Piecewise Constant Argument

Department of Computer Science, Guangdong Polytechnic Normal University, Guangzhou 510665, Guangdong, China

Received 17 August 2012; Revised 27 October 2012; Accepted 20 November 2012

Academic Editor: Samir H. Saker

Copyright © 2012 Haihua Liang and Gen-qiang Wang. 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. O. Došlý and A. Lomtatidze, “Oscillation and nonoscillation criteria for half-linear second order differential equations,” Hiroshima Mathematical Journal, vol. 36, no. 2, pp. 203–219, 2006. View at Zentralblatt MATH
  3. 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
  4. 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
  5. K. L. Cooke and J. Wiener, “A survey of differential equations with piecewise continuous arguments,” in Delay Differential Equations and Dynamical Systems, vol. 1475 of Lecture Notes in Mathematics, pp. 1–15, Springer, Berlin, Germany, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. A. R. Aftabizadeh and J. Wiener, “Oscillatory properties of first order linear functional-differential equations,” Applicable Analysis, vol. 20, no. 3-4, pp. 165–187, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. A. R. Aftabizadeh, J. Wiener, and J.-M. Xu, “Oscillatory and periodic solutions of delay differential equations with piecewise constant argument,” Proceedings of the American Mathematical Society, vol. 99, no. 4, pp. 673–679, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. H. A. Agwo, “Necessary and sufficient conditions for the oscillation of delay differential equation with a piecewise constant argument,” International Journal of Mathematics and Mathematical Sciences, vol. 21, no. 3, pp. 493–497, 1998. View at Publisher · View at Google Scholar
  9. Z. Luo and J. Shen, “New results on oscillation for delay differential equations with piecewise constant argument,” Computers & Mathematics with Applications, vol. 45, no. 12, pp. 1841–1848, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. G.-Q. Wang and S. S. Cheng, “Oscillation of second order differential equation with piecewise constant argument,” Cubo, vol. 6, no. 3, pp. 55–63, 2004. View at Zentralblatt MATH
  11. S. M. Shan and J. Wiener, “Advanced differential equations with piecewise constant argument deviations,” International Journal of Mathematics and Mathematical Sciences, vol. 6, pp. 55–63, 1983.
  12. A. Škerlík, “Oscillation theorems for third order nonlinear differential equations,” Mathematica Slovaca, vol. 42, no. 4, pp. 471–484, 1992. View at Zentralblatt MATH
  13. A. Kneser, “Untersuchungen über die reellen Nullstellen der Integrale linearer Differentialgleichungen,” Mathematische Annalen, vol. 42, no. 3, pp. 409–435, 1893. View at Publisher · View at Google Scholar