On the asymptotic behavior of solutions of Emden-Fowler equations on time scales

Consider the Emden-Fowler dynamic equation x(Delta Delta)(t) + p(t)x(alpha)(t) = 0, alpha > 0, (0.1) where p is an element of C-rd ([t(0), infinity)(T), R), alpha is the quotient of odd positive integers, and T denotes a time scale which is unbounded above and satisfies an additional condition (C) given below. We prove that if integral(infinity)(t0) t(alpha)vertical bar p(t)vertical bar Delta t < infinity (and when alpha = 1 we also assume lim(t ->infinity) tp(t)mu(t) = 0), then (0.1) has a solution x(t) with the property that lim(t ->infinity) x(t)/t = A not equal 0.