Abstract
This article comes up with criteria to make sure that the solutions to superlinear, half-linear, and noncanonical dynamic equations oscillate in both advanced and delayed cases; these criteria are comparable to the Hille-type and Ohriska-type criteria for the canonical nonlinear dynamic equations; and also these results solve an open problem in many existing works in the literature on dynamic equations. To demonstrate the importance of the results, some examples have been introduced.