Advances in Difference Equations
Volume 2008 (2008), Article ID 458687, 12 pages
Research Article

Iterated Oscillation Criteria for Delay Dynamic Equations of First Order

M. Bohner,1 B. Karpuz,2 and Ö. Öcalan2

1Department of Economics and Finance, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA
2Department of Mathematics, Faculty of Science and Arts, Afyon Kocatepe University, ANS Campus, 03200 Afyonkarahisar, Turkey

Received 9 June 2008; Accepted 4 December 2008

Academic Editor: John Graef

Copyright © 2008 M. Bohner 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.


We obtain new sufficient conditions for the oscillation of all solutions of first-order delay dynamic equations on arbitrary time scales, hence combining and extending results for corresponding differential and difference equations. Examples, some of which coincide with well-known results on particular time scales, are provided to illustrate the applicability of our results.