On Unbounded Positive Solutions of Second-Order Difference Equations with a Singular Nonlinear Term

AbstractIn this paper, several necessary and/or sufficient conditions are given for the existence of unbounded positive solutions of nonlinear difference equations of the formΔrnΔxn+fn,xn=0,n∈Nn0,where N(n0)={n0,n0+1,…,} (n0 is a fixed nonnegative integer), rn>0 for n≥n0 such that ∑∞n=n01/rn=∞, and f: N(n0)×R→R is a real-valued continuous function such that f(n,x)≥0 for all (n,x)∈N(n0)×(0,∞)