Monotone solutions of a class of nonlinear difference equations (Q1334563)

The authors prove some comparison theorems for the existence of a positive nondecreasing solution of the nonlinear difference equation (1) \(\Delta (p_{k - 1} (\Delta x_{k - 1})^ \sigma) + q_ k x^ \sigma_ k = 0\), \(k = 1,2, \dots\) where \(\sigma > 0\) and \(\{p_ k\}^ \infty_ 0\) is a positive sequence. Sufficient conditions for the nonexistence of positive nondecreasing solutions of equation (1) are given. For equation (1) with \(p_{k - 1} \equiv 1\) the authors obtain conditions for the existence of positive increasing solutions which converge to a finite limit.