International Journal of Differential Equations
Volume 2010 (2010), Article ID 308357, 14 pages
doi:10.1155/2010/308357
Research Article

Oscillation Criteria for Even Order Neutral Equations with Distributed Deviating Argument

Department of Mathematics, Qufu Normal University, Qufu 273165, China

Received 24 September 2009; Accepted 24 November 2009

Academic Editor: Leonid Berezansky

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 present new oscillation criteria for the even order neutral delay differential equations with distributed deviating argument [r(t)ψ(x(t))Z(n1)(t)]+abp(t,ξ)f[x(g(t,ξ))]dσ(ξ)=0,  tt0, where Z(t)=x(t)+q(t)x(tτ). Assumptions in our theorems are less restrictive, whereas the proofs are significantly simpler compared to those by Wang et al. (2005).