Applicable Analysis and Discrete Mathematics Oscillation Criteria for First Order Forced Dynamic Equations

We obtain some new oscillation criteria for solutions to certain first order forced dynamic equations on a time scale T of the form x ∆ (t) + r(t)Φγ (x σ (t)) + p(t)Φα (x σ (t)) + q(t)Φ β (x σ (t)) = f (t), with Φη (u) := |u| η−1 u, η > 0. Here r(t), p (t) , q(t) and f (t) are rd-continuous functions on T and the forcing term f (t) is not required to be the derivative of an oscillatory function. Our results in the special cases when T = R and T = N involve and improve some previous oscillation results for first-order differential and difference equations. An example illustrating the importance of our results is also included.