Advances in Difference Equations
Volume 2009 (2009), Article ID 756171, 13 pages
doi:10.1155/2009/756171
Research Article

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

Zhenlai Han,1,2 Tongxing Li,2 Shurong Sun,2 and Chenghui Zhang1

1School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China
2School of Science, University of Jinan, Jinan, Shandon 250022, China

Received 6 December 2008; Revised 27 February 2009; Accepted 25 May 2009

Academic Editor: Alberto Cabada

Copyright © 2009 Zhenlai Han 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 nonlinear delay dynamic equations (r(t)(xΔ(t))γ)Δ+p(t)f(x(τ(t)))=0 on a time scale 𝕋; here γ>0 is a quotient of odd positive integers with r and p real-valued positive rd-continuous functions defined on 𝕋. Our results not only extend some results established by Hassan in 2008 but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation.