Advances in Difference Equations
Volume 2010 (2010), Article ID 873459, 22 pages
doi:10.1155/2010/873459
Research Article

Nonoscillation of First-Order Dynamic Equations with Several Delays

Elena Braverman1 and Başak Karpuz2

1Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N. W., Calgary, AB, T2N 1N4, Canada
2Department of Mathematics, Faculty of Science and Arts, ANS Campus, Afyon Kocatepe University, 03200 Afyonkarahisar, Turkey

Received 18 February 2010; Accepted 21 July 2010

Academic Editor: John Graef

Copyright © 2010 Elena Braverman and Başak Karpuz. 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

For dynamic equations on time scales with positive variable coefficients and several delays, we prove that nonoscillation is equivalent to the existence of a positive solution for the generalized characteristic inequality and to the positivity of the fundamental function. Based on this result, comparison tests are developed. The nonoscillation criterion is illustrated by examples which are neither delay-differential nor classical difference equations.