Abstract
We obtain some new oscillation criteria for solutions to certain first order forced dynamic equations on a time scale T of the form
x(Delta)(t) + r(t)phi(gamma) (x(sigma) (t)) + p (t)phi(alpha) (x(sigma) (t)) + q(t)phi(beta)(x(sigma) (t)) = f (t),
with phi(eta) (u) := vertical bar u vertical bar(n-1) u, eta > 0. Here r (t); p (t); q (t) and f (t) are rdcontinuous 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.