Hindawi Publishing Corporation Advances in Difference Equations Volume 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 Chen 1 1 School of Science, University of Jinan, Jinan, Shandong 250022, China 2 School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China 3 Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA Correspondence should be addressed to Zhenlai Han, hanzhenlai@163.com Received 10 December 2009; Revised 22 June 2010; Accepted 1 July 2010 Academic Editor: A ˘ gacık Zafer Copyright q 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. 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 ≥ t 0 , where 0 ≤ pt ≤ p 0 < ∞. 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. 1. Introduction In recent years, the oscillatory behavior of differential equations has been the subject of intensive study; we refer to the articles 1–13; Especially, the study of the oscillation of neutral delay differential equations is of great interest in the last three decades; see for example 14–38 and references cited therein. Second-order neutral delay differential equations have applications in problems dealing with vibrating masses attached to an elastic bar and in some variational problems see 39. This paper is concerned with the oscillatory behavior of the second-order neutral delay differential equation ( xt ptxτ t ) ′′  qtf xσ t  0, t ≥ t 0 , 1.1 where p, q ∈ Ct 0 , ∞, R,f ∈ CR, R. Throughout this paper, we assume that