Advances in Difference Equations
Volume 2010 (2010), Article ID 289340, 8 pages
doi:10.1155/2010/289340
Research Article

On the Oscillation of Second-Order Neutral Delay Differential Equations

Zhenlai Han,1,2 Tongxing Li,1 Shurong Sun,1,3 and Weisong Chen1

1School of Science, University of Jinan, Jinan, Shandong 250022, China
2School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China
3Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, China

Received 8 October 2009; Accepted 10 January 2010

Academic Editor: Toka Diagana

Copyright © 2010 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

Some new oscillation criteria for the second-order neutral delay differential equation (r(t)z′(t))′+q(t)x(σ(t))=0, t≥t0 are established, where ∫t0∞(1/r(t))dt=∞, z(t)=x(t)+p(t)x(τ(t)), 0≤p(t)≤p0<∞, q(t)>0. These oscillation criteria extend and improve some known results. An example is considered to illustrate the main results.