Advances in Difference Equations
Volume 2006 (2006), Article ID 65626, 9 pages

Oscillation of second-order neutral delay and mixed-type dynamic equations on time scales

Y. Şahİner

Department of Mathematics , Atilim University, Incek-Ankara 06836, Turkey

Received 31 January 2006; Revised 11 May 2006; Accepted 15 May 2006

Copyright © 2006 Y. Şahİner. 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.


We consider the equation (r(t)(yΔ(t))γ)Δ+f(t,x(δ(t)))=0, tT, where y(t)=x(t)+p(t)x(τ(t)) and γ is a quotient of positive odd integers. We present some sufficient conditions for neutral delay and mixed-type dynamic equations to be oscillatory, depending on deviating arguments τ(t) and δ(t), tT.