Abstract
In this paper, we study the third-order functional dynamic equations with gamma-Laplacian and nonlinearities given by Riemann-Stieltjes integrals
{r(2)(t) phi(gamma 2) ([r(1)(t) phi(gamma 1) (x(Delta) (t))](Delta))}(Delta) + integral(b)(a) q (t, s) phi(alpha(s)) (x(g(t, s))) d zeta (s) = 0,
on an above-unbounded time scale T, where phi(gamma)(u) := |u|(gamma-1) u and integral(b)(a) f (s) d zeta (s) denotes the Riemann-Stieltjes integral of the function f on [a, b] with respect to zeta. Results are obtained for the asymptotic and oscillatory behavior of the solutions. This work extends and improves some known results in the literature on third order nonlinear dynamic equations.