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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 173158, 6 pages
http://dx.doi.org/10.1155/2011/173158
Research Article

On Delay-Independent Criteria for Oscillation of Higher-Order Functional Differential Equations

School of Mathematics, University of Jinan, Jinan, Shandong 250022, China

Received 20 March 2011; Accepted 8 May 2011

Academic Editor: Pavel Drábek

Copyright © 2011 Yuangong Sun. 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 investigate the oscillation of the following higher-order functional differential equation: ๐‘ฅ(๐‘›)(๐‘ก)+๐‘ž(๐‘ก)|๐‘ฅ(๐‘กโˆ’๐œ)|๐œ†โˆ’1๐‘ฅ(๐‘กโˆ’๐œ)=๐‘’(๐‘ก), where ๐‘ž(๐‘ก) and ๐‘’(๐‘ก) are continuous functions on [๐‘ก0,โˆž), 1>๐œ†>0 and ๐œโ‰ 0 are constants. Unlike most of delay-dependent oscillation results in the literature, two delay-independent oscillation criteria for the equation are established in both the case ๐œ>0 and the case ๐œ<0 under the assumption that the potentials ๐‘ž(๐‘ก) and ๐‘’(๐‘ก) change signs on [๐‘ก0,โˆž).