Advances in Difference Equations
Volume 2005 (2005), Issue 3, Pages 345-367
doi:10.1155/ADE.2005.345

On the oscillation of certain third-order difference equations

Ravi P. Agarwal,1 Said R. Grace,2 and Donal O'Regan3

1Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901-6975, FL, USA
2Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Orman, Giza 12221, Egypt
3Department of Mathematics, National University of Ireland, Galway, University Road, Galway, Ireland

Received 28 August 2004

Copyright © 2005 Ravi P. Agarwal 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 establish some new criteria for the oscillation of third-order difference equations of the form Δ((1/a2(n))(Δ(1/a1(n))(Δx(n))α1)α2)+δq(n)f(x[g(n)])=0, where Δ is the forward difference operator defined by Δx(n)=x(n+1)−x(n).