Unbounded positive solutions of higher-order difference equations with singular nonlinear term

In this paper, several necessary and/or sufficient conditions are given for the existence of unbounded positive solutions of nonlinear difference equa tions of the form Delta(m)x(n-1) + sigma f(n,x(n-r)) = 0, n is an element of N-0, where m greater than or equal to 2, sigma = +1, or sigma = -1, and f : N-0 x R --> R is a real-valued continuous function such that f(n,x) greater tha n or equal to 0 for all (n,x) is an element of N-0 x (0,infinity), where N- 0 = {0,1,...}. (C) 2000 Elsevier Science Ltd. All rights reserved.