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.
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.