Abstract
In this paper, we study the third-order functional dynamic equation
{r(2)(t)phi(alpha 2)([r(1)(t)phi(alpha 1)(x(Delta)(t))](Delta))}(Delta) + q(t)phi(alpha)(x(g(t))) = 0,
on an upper-unbounded time scale T. We will extend the so-called Hille and Nehari type criteria to third-order dynamic equations on time scales. This work extends and improves some known results in the literature on third-order nonlinear dynamic equations and the results are established for a time scale T without assuming certain restrictive conditions on T. Some examples are given to illustrate the main results.