Advances in Difference Equations
Volume 2010 (2010), Article ID 184180, 9 pages
doi:10.1155/2010/184180
Research Article

Oscillation of Even-Order Neutral Delay Differential Equations

Tongxing Li,1 Zhenlai Han,1,2 Ping Zhao,3 and Shurong Sun1,4

1School of Science, University of Jinan, Jinan, Shandong 250022, China
2School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China
3School of Control Science and Engineering, University of Jinan, Jinan, Shandong 250022, China
4Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA

Received 28 November 2009; Revised 31 January 2010; Accepted 29 March 2010

Academic Editor: Josef Diblik

Copyright © 2010 Tongxing Li 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 using Riccati transformation technique, we will establish some new oscillation criteria for the even order neutral delay differential equations [z(t)](n)+q(t)f(x(σ(t)))=0, t≥t0, where n is even, z(t)=x(t)+p(t)x(τ(t)), 0≤p(t)≤p0<∞, and q(t)≥0. These oscillation criteria, at least in some sense, complement and improve those of Zafer (1998) and Zhang et al. (2010). An example is considered to illustrate the main results.