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. Agarwal1
, Said R. Grace2
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
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).