Advances in Difference Equations
Volume 2010 (2010), Article ID 450264, 24 pages
doi:10.1155/2010/450264
Oscillatory behavior of quasilinear neutral delay dynamic equations on time scales
Zhenlai Han1
, Shurong Sun1
, Tongxing Li1
and Chenghui Zhang4
1School of Science, University of Jinan, Jinan, Shandong 250022, China
4School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China
Abstract
By means of the averaging technique and the generalized Riccati transformation technique, we establish some oscillation criteria for the second-order quasilinear neutral delay dynamic equations [r(t)|xΔ(t)|γ-1xΔ(t)]Δ+q1(t)|y(δ1(t))|α-1y(δ1(t))+q2(t)|y(δ2(t))|β-1y(δ2(t))=0, t∈[t0,∞)𝕋, where x(t)=y(t)+p(t)y(τ(t)), and the time scale interval is [t0,∞)𝕋:=[t0,∞)∩𝕋. Our results in this paper not only extend the results given by Agarwal et al. (2005) but also unify the oscillation of the second-order neutral delay differential equations and the second-order neutral delay difference equations.