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 equations of the form ΔmXn-1+σf(n,xn−τ)=0, n N0, where m ≥ 2, σ = +1, or σ = −1, and f : N0 × R → R is a real-valued continuous function such that f(n,x) ≥ 0 for all (n,x) N0 × (0, ∞), where N0 = (0, 1,) ….