Advances in Difference Equations
Volume 2009 (2009), Article ID 756171, 13 pages
doi:10.1155/2009/756171
Oscillation for second-order nonlinear delay dynamic equations on time scales
Zhenlai Han1
, Tongxing Li2
, Shurong Sun2
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
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.