The authors consider linear delay dynamic equations
on a time scale , i.e., a closed subset of the reals, which is assumed to be unbounded above. Moreover, is supposed to be regressive, rd-continuous, and satisfies for all . Using a necessary condition for the existence of an eventually periodic solution, an oscillation criterion for is obtained. Furthermore, the authors deduce sufficient conditions for the existence of positive solutions, and for the oscillatory behavior of a nonhomogeneous version of .
These criteria generalize well known results for ordinary differential and difference equations to dynamic equations on time scales.