Abstract
In this paper, we study the nth-order ha linear dynamic equations
(x([n-1]))(Delta) (t) + p(t)phi(alpha[1,n-1]) (x(g(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) san u, and alpha[i,j] := alpha i ... alpha j Criteria are obtained for the asymptotics and oscillation of solutions for both even and odd order cases. This work extends several known results in the literature on second-order, third-order, and higher-order linear and half-linear dynamic equations.