Abstract and Applied Analysis
Volume 2011 (2011), Article ID 387483, 9 pages
doi:10.1155/2011/387483
Research Article

Oscillation Criteria for Certain Second-Order Nonlinear Neutral Differential Equations of Mixed Type

1School of Science, University of Jinan, Jinan, Shandong 250022, China
2School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China

Received 19 September 2010; Accepted 19 January 2011

Academic Editor: Josef Diblík

Copyright © 2011 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 oscillation criteria are established for the second-order nonlinear neutral differential equations of mixed type [ ( 𝑥 ( 𝑡 ) + 𝑝 1 𝑥 ( 𝑡 𝜏 1 ) + 𝑝 2 𝑥 ( 𝑡 + 𝜏 2 ) ) 𝛾 ] = 𝑞 1 ( 𝑡 ) 𝑥 𝛾 ( 𝑡 𝜎 1 ) + 𝑞 2 ( 𝑡 ) 𝑥 𝛾 ( 𝑡 + 𝜎 2 ) , 𝑡 𝑡 0 , where 𝛾 1 is a quotient of odd positive integers. Our results generalize the results given in the literature.