Advances in Difference Equations
Volume 2010 (2010), Article ID 763278, 23 pages
doi:10.1155/2010/763278
Research Article

Oscillation Criteria for Second-Order Nonlinear Neutral Delay Differential Equations

Zhenlai Han,1,2 Tongxing Li,1,2 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, USA

Received 10 December 2009; Revised 22 June 2010; Accepted 1 July 2010

Academic Editor: Ağacık Zafer

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 sufficient conditions are established for the oscillation of second-order neutral differential equation (x(t)+p(t)x(τ(t)))′′+q(t)f(x(σ(t)))=0, t≥t0, where 0≤p(t)≤p0<+∞. The results complement and improve those of Grammatikopoulos et al. Ladas, A. Meimaridou, Oscillation of second-order neutral delay differential equations, Rat. Mat. 1 (1985), Grace and Lalli (1987), Ruan (1993), H. J. Li (1996), H. J. Li (1997), Xu and Xia (2008).