Abstract
We will consider the higher order functional dynamic equations with mixed nonlinearities of the form x([n])(t) + Sigma(N)(j=0) p(j)(t)phi(gamma j)(x(phi(j)(t))) = 0, on an above-unbounded time scale T, where n >= 2, x([i])(t) = r(i)(t)phi(alpha i)[(x([i-1]))(Delta)(t)], i = 1, ..., n - 1, with x([0]) = x, phi(beta)(u) = vertical bar u vertical bar(beta) sgn u, and alpha[i, j] = alpha(i) ... alpha(j). The function phi(i) : T -> T is a rd-continuous function such that lim(t ->infinity)phi(i)(t) = infinity for j = 0, 1, ..., N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.