Copyright © 2011 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.
Existence of nonoscillatory solutions for the second-order dynamic equation for is investigated in this paper. The results involve nonoscillation criteria in terms of relevant dynamic and generalized characteristic inequalities, comparison theorems, and explicit nonoscillation and oscillation conditions. This allows to obtain most known nonoscillation results for second-order delay differential equations in the case
for and for second-order nondelay difference equations ( for ). Moreover, the general results imply new nonoscillation tests for delay differential equations with arbitrary and for second-order delay difference equations. Known nonoscillation results for quantum scales can also be deduced.