Summary: Recently, S. S. Cheng and W. T. Patula [Nonlinear Anal., Theory Methods Appl. 20, No. 3, 193-203 (1993; Zbl 0774.39001)] established the existence of a positive nondecreasing solution to a nonlinear difference equation arising from Hardy’s inequality by Schauder’s fixed point theorem. In this paper, we give a new sufficient condition, under which the nonlinear difference equation has at least one positive nondecreasing solution. The arguments are based on the fixed point theorems of increasing operators.