Abstract
The purpose of this work is to derive sufficient conditions for the oscillation of all solutions of the third-order functional dynamic equation {p(2)(xi)phi(gamma 2 )([p(1 )(xi phi(gamma 1)(y(delta){xi))](delta)]}(delta)+p(xi)phi(beta)(y(g(xi)))=0, on a time scale T. In addition, we present some Hille-type conditions for generalized third-order dynamic equations that improve and extend significant contributions reported in the literature without imposing time-scale restrictions. An example is given to demonstrate the essential results.