On Unbounded Positive Solutions of Second-Order Difference Equations with a Singular Nonlinear Term1

In this paper, several necessary andror sufficient conditions are given for the existence of unbounded positive solutions of nonlinear difference equations of the form D rnD xn.qf n, xn.s0, ngN n0., where N n0.s n0, n0q1, . . . ,4 n0 is a fixed nonnegative integer., rn)0 for nGn0 such that `nsn0 1rrns`, and f : N n0.=RªR is a real-valued continu- ous function such that f n, x.G0 for all n, x.gN n0.= 0, `..