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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 740568, 11 pages
http://dx.doi.org/10.1155/2013/740568
Research Article

Oscillation Criteria for Fourth-Order Nonlinear Dynamic Equations on Time Scales

1College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China
2Department of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi 530003, China

Received 6 May 2013; Revised 20 June 2013; Accepted 21 June 2013

Academic Editor: Delfim F. M. Torres

Copyright © 2013 Xin Wu 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. V. Kac and P. Cheung, Quantum Calculus, Universitext, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  3. M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, Mass, USA, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, Mass, USA, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. T. Sun, H. Xi, and X. Peng, “Asymptotic behavior of solutions of higher-order dynamic equations on time scales,” Advances in Difference Equations, vol. 2011, Article ID 237219, 14 pages, 2011. View at Zentralblatt MATH · View at MathSciNet
  6. T. Sun, H. Xi, X. Peng, and W. Yu, “Nonoscillatory solutions for higher-order neutral dynamic equations on time scales,” Abstract and Applied Analysis, vol. 2010, Article ID 428963, 16 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. T. Sun, H. Xi, and W. Yu, “Asymptotic behaviors of higher order nonlinear dynamic equations on time scales,” Journal of Applied Mathematics and Computing, vol. 37, no. 1-2, pp. 177–192, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  8. T. Sun, W. Yu, and H. Xi, “Oscillatory behavior and comparison for higher order nonlinear dynamic equations on time scales,” Journal of Applied Mathematics & Informatics, vol. 30, no. 1-2, pp. 289–304, 2012. View at Zentralblatt MATH · View at MathSciNet
  9. T. S. Hassan, “Oscillation of third order nonlinear delay dynamic equations on time scales,” Mathematical and Computer Modelling, vol. 49, no. 7-8, pp. 1573–1586, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. L. Erbe, A. Peterson, and S. H. Saker, “Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales,” Journal of Computational and Applied Mathematics, vol. 181, no. 1, pp. 92–102, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. L. Erbe, A. Peterson, and S. H. Saker, “Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation,” The Canadian Applied Mathematics Quarterly, vol. 14, no. 2, pp. 129–147, 2006. View at Zentralblatt MATH · View at MathSciNet
  12. L. Erbe, A. Peterson, and S. H. Saker, “Hille and Nehari type criteria for third-order dynamic equations,” Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 112–131, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. T. Li, Z. Han, S. Sun, and Y. Zhao, “Oscillation results for third order nonlinear delay dynamic equations on time scales,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 34, no. 3, pp. 639–648, 2011. View at Zentralblatt MATH · View at MathSciNet
  14. Y. Wang and Z. Xu, “Asymptotic properties of solutions of certain third-order dynamic equations,” Journal of Computational and Applied Mathematics, vol. 236, no. 9, pp. 2354–2366, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. L. Erbe, T. S. Hassan, and A. Peterson, “Oscillation of third order nonlinear functional dynamic equations on time scales,” Differential Equations and Dynamical Systems, vol. 18, no. 1-2, pp. 199–227, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Y. Qi and J. Yu, “Oscillation criteria for fourth-order nonlinear delay dynamic equations,” Electronic Journal of Differential Equations, vol. 2013, no. 79, pp. 1–17, 2013.
  17. S. R. Grace, M. Bohner, and S. Sun, “Oscillation of fourth-order dynamic equations,” Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 4, pp. 545–553, 2010. View at Zentralblatt MATH · View at MathSciNet
  18. S. R. Grace, S. Sun, and Y. Wang, “On the oscillation of fourth order strongly superlinear and strongly sublinear dynamic equations,” Journal of Applied Mathematics and Computing, 2013. View at Publisher · View at Google Scholar
  19. R. P. Agarwal, M. Bohner, T. Li, and C. Zhang, “Oscillation theorems for fourth-order half-linear delay dynamic equations with damping,” Mediterranean Journal of Mathematics, 2013. View at Publisher · View at Google Scholar
  20. 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