Advances in Difference Equations
Volume 2010 (2010), Article ID 642356, 15 pages
doi:10.1155/2010/642356
Research Article
Oscillation for a Class of Second-Order Emden-Fowler Delay Dynamic Equations on Time Scales
1School of Science, University of Jinan, Jinan, Shandong 250022, China
2Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA
3School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China
4School of Control Science and Engineering, University of Jinan, Jinan, Shandong 250022, China
Received 13 December 2009; Accepted 4 March 2010
Academic Editor: Leonid Berezansky
Copyright © 2010 Shurong Sun 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.
Abstract
By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order Emden-Fowler delay dynamic equations (rxΔ)Δ(t)+p(t)xγ(τ(t))=0 on a time scale 𝕋; here γ is a quotient of odd positive integers with r and p as real-valued positive rd-continuous functions defined on 𝕋. Our results in this paper not only extend the results given in Agarwal et al. (2005), Akin-Bohner et al. (2007) and Han et al. (2007) but also unify the results about oscillation of the second-order Emden-Fowler delay differential equation and the second-order Emden-Fowler delay difference equation.