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Abstract and Applied Analysis
Volume 2014, Article ID 475428, 5 pages
http://dx.doi.org/10.1155/2014/475428
Research Article

New Oscillatory Behavior of Second-Order Nonlinear Dynamic Equations with Damping on Time Scales

Department of Mathematics, Binzhou University, Shandong 256603, China

Received 21 April 2014; Revised 28 May 2014; Accepted 29 May 2014; Published 9 June 2014

Academic Editor: Tongxing Li

Copyright © 2014 Shouhua Liu and Quanxin Zhang. 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. R. Grace, M. Bohner, and R. P. Agarwal, “On the oscillation of second-order half-linear dynamic equations,” Journal of Difference Equations and Applications, vol. 15, no. 5, pp. 451–460, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. R. P. Agarwal, M. Bohner, and S. H. Saker, “Oscillation of second order delay dynamic equations,” Canadian Applied Mathematics Quarterly, vol. 13, pp. 1–18, 2005. View at Google Scholar · View at Zentralblatt MATH
  3. 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 · View at Zentralblatt MATH · View at Scopus
  4. 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 Scopus
  5. 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 Scopus
  6. L. Erbe, T. S. Hassan, and A. Peterson, “Oscillation criteria for nonlinear functional neutral dynamic equations on time scales,” Journal of Difference Equations and Applications, vol. 15, no. 11-12, pp. 1097–1116, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. S. R. Grace, R. P. Agarwal, B. Kaymakçalan, and W. Sae-Jie, “Oscillation theorems for second order nonlinear dynamic equations,” Journal of Applied Mathematics and Computing, vol. 32, no. 1, pp. 205–218, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. Q. Zhang and L. Gao, “Oscillation of second-order nonlinear delay dynamic equations with damping on time scales,” Journal of Applied Mathematics and Computing, vol. 37, no. 1-2, pp. 145–158, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. 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 MathSciNet
  10. R. P. Agarwal, M. Bohner, S. R. Grace, and D. O’Regan, Discrete Oscillation Theory, Hindawi, New York, NY, USA, 2005.
  11. M. Bohner, “Some oscillation criteria for first order delay dynamic equations,” Far East Journal of Applied Mathematics, vol. 18, no. 3, pp. 289–304, 2005. View at Google Scholar · View at Zentralblatt MATH