After the fashion of Uri Elias, we analyze the characteristics of extremal solutions for linear difference equations of the form Ly(t) + p(t) y(t) = 0, where L is an nth order disconjugate linear difference operator given its Pólya-Hartman factorization, and where p(t) is nonzero and of constant sign on the interval I = [a, ∞) = {a, a + 1, …}. This work is based on and extends the work concerning the classification of solutions done by Allan Peterson and Darrel Hankerson.