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International Journal of Differential Equations
Volume 2010 (2010), Article ID 181784, 15 pages
doi:10.1155/2010/181784
Research Article

Oscillation Theorems for Second-Order Forced Neutral Nonlinear Differential Equations with Delayed Argument

Jing Shao1,2 and Fanwei Meng2

1Department of Mathematics, Jining University, Qufu, Shandong 273155, China
2School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China

Received 13 October 2009; Accepted 14 December 2009

Academic Editor: Elena Braverman

Copyright © 2010 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 are concerned with the oscillation of the forced second-order neutral nonlinear differential equations with delayed argument in the form ( 𝑟 ( 𝑡 ) ( 𝑥 ( 𝑡 ) + 𝑎 ( 𝑡 ) 𝑥 ( 𝜎 ( 𝑡 ) ) ) ) ∑ + 𝑝 ( 𝑡 ) 𝑓 ( 𝑥 ( 𝜏 ( 𝑡 ) ) ) + 𝑛 𝑖 = 1 𝑞 𝑖 ( 𝑡 ) | 𝑥 ( 𝑡 ) | 𝜆 𝑖 s n g 𝑥 ( 𝑡 ) = 𝑒 ( 𝑡 ) . No restriction is imposed on the potentials 𝑝 ( 𝑡 ) , 𝑞 𝑖 ( 𝑡 ) , and 𝑒 ( 𝑡 ) to be nonnegative. Our methodology is somewhat different from those of previous authors.