Advances in Difference Equations
Volume 2010 (2010), Article ID 512437, 14 pages
doi:10.1155/2010/512437
Research Article

Oscillation Criteria for Second-Order Quasilinear Neutral Delay Dynamic Equations on Time Scales

Yibing Sun,1 Zhenlai Han,1,2 Tongxing Li,1 and Guangrong Zhang1

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

Received 25 January 2010; Accepted 24 February 2010

Academic Editor: Gaston Mandata N'Guerekata

Copyright © 2010 Yibing 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

We establish some new oscillation criteria for the second-order quasilinear neutral delay dynamic equations [r(t)(zΔ(t))γ]Δ+q1(t)xα(τ1(t))+q2(t)xβ(τ2(t))=0 on a time scale 𝕋, where z(t)=x(t)+p(t)x(τ0(t)), 0<α<γ<β. Our results generalize and improve some known results for oscillation of second-order nonlinear delay dynamic equations on time scales. Some examples are considered to illustrate our main results.