Abstract and Applied Analysis
Volume 2011 (2011), Article ID 927690, 15 pages
doi:10.1155/2011/927690
Research Article

Oscillation of Second-Order Neutral Functional Differential Equations with Mixed Nonlinearities

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

Received 2 September 2010; Revised 26 November 2010; Accepted 23 December 2010

Academic Editor: Miroslava Růžičková

Copyright © 2011 Shurong 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 study the following second-order neutral functional differential equation with mixed nonlinearities ( 𝑟 ( 𝑡 ) | ( 𝑢 ( 𝑡 ) + 𝑝 ( 𝑡 ) 𝑢 ( 𝑡 𝜎 ) ) | 𝛼 1 ( 𝑢 ( 𝑡 ) + 𝑝 ( 𝑡 ) 𝑢 ( 𝑡 𝜎 ) ) ) + 𝑞 0 ( 𝑡 ) | 𝑢 ( 𝜏 0 ( 𝑡 ) ) | 𝛼 1 𝑢 ( 𝜏 0 ( 𝑡 ) ) + 𝑞 1 ( 𝑡 ) | 𝑢 ( 𝜏 1 ( 𝑡 ) ) | 𝛽 1 𝑢 ( 𝜏 1 ( 𝑡 ) ) + 𝑞 2 ( 𝑡 ) | 𝑢 ( 𝜏 2 ( 𝑡 ) ) | 𝛾 1 𝑢 ( 𝜏 2 ( 𝑡 ) ) = 0 , where 𝛾 > 𝛼 > 𝛽 > 0 , 𝑡 0 ( 1 / 𝑟 1 / 𝛼 ( 𝑡 ) ) d 𝑡 < . Oscillation results for the equation are established which improve the results obtained by Sun and Meng (2006), Xu and Meng (2006), Sun and Meng (2009), and Han et al. (2010).