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International Journal of Differential Equations
Volume 2011 (2011), Article ID 863801, 15 pages
http://dx.doi.org/10.1155/2011/863801
Research Article

Oscillation of Second-Order Nonlinear Delay Dynamic Equations on Time Scales

Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

Received 3 May 2011; Accepted 6 June 2011

Academic Editor: Elena Braverman

Copyright © 2011 H. A. Agwa 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. S. Hilger, “Analysis on measure chains—a unified approach to continuous and discrete calculus,” Results in Mathematics, vol. 18, no. 1-2, pp. 18–56, 1990. View at Zentralblatt MATH
  2. R. Agarwal, M. Bohner, D. O'Regan, and A. Peterson, “Dynamic equations on time scales: a survey,” Journal of Computational and Applied Mathematics, vol. 141, no. 1-2, pp. 1–26, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. M. Bohner and A. Peterson, Dynamic Equations on Time Scales, Birkhäuser Boston Inc., Boston, Mass, USA, 2001, An introduction with application.
  4. M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser Boston Inc., Boston, Mass, USA, 2003.
  5. V. Kac and P. Cheung, Quantum Calculus, Universitext, Springer, New York, NY, USA, 2002.
  6. R. P. Agarwal, M. Bohner, and S. H. Saker, “Oscillation of second order delay dynamic equations,” The Canadian Applied Mathematics Quarterly, vol. 13, no. 1, pp. 1–18, 2005. View at Zentralblatt MATH
  7. R. P. Agarwal, D. O'Regan, and S. H. Saker, “Philos-type oscillation criteria for second order half-linear dynamic equations on time scales,” The Rocky Mountain Journal of Mathematics, vol. 37, no. 4, pp. 1085–1104, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. Bohner and S. H. Saker, “Oscillation of second order nonlinear dynamic equations on time scales,” The Rocky Mountain Journal of Mathematics, vol. 34, no. 4, pp. 1239–1254, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. L. Erbe, A. Peterson, and S. H. Saker, “Oscillation criteria for second-order nonlinear dynamic equations on time scales,” Journal of the London Mathematical Society. Second Series, vol. 67, no. 3, pp. 701–714, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Q. Zhang, L. Gao, and L. Wang, “Oscillation of second-order nonlinear delay dynamic equations on time scales,” Computers and Mathematics with Applications, vol. 61, no. 8, pp. 2342–2348, 2011. View at Publisher · View at Google Scholar
  11. S. R. Grace, R. P. Agarwal, M. Bohner, and D. O'Regan, “Philos type criteria for second-order half-linear dynamic equations,” Mathematical Inequalities and Applications, vol. 14, no. 1, pp. 211–222, 2011.
  12. S. Sun, Z. Han, and C. Zhang, “Oscillation of second-order delay dynamic equations on time scales,” Journal of Applied Mathematics and Computing, vol. 30, no. 1-2, pp. 459–468, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. L. Erbe, A. Peterson, and S. H. Saker, “Oscillation criteria for second-order nonlinear delay dynamic equations,” Journal of Mathematical Analysis and Applications, vol. 333, no. 1, pp. 505–522, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Y. Şahiner, “Oscillation of second-order delay differential equations on time scales,” Nonlinear Analysis, Theory, Methods and Applications, vol. 63, no. 5–7, pp. e1073–e1080, 2005. View at Publisher · View at Google Scholar
  15. T. S. Hassan, “Oscillation criteria for half-linear dynamic equations on time scales,” Journal of Mathematical Analysis and Applications, vol. 345, no. 1, pp. 176–185, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge Mathematical Library, Cambridge University Press, Cambridge, UK, 1988.