Abstract

The aim of this paper is to show that the following difference equation: xn+1=α+(xn−kxn−m)p,n=0,1,2,..., where α > −1, p > 0, k,m ∈ N are fixed, 0 ≤ m < k, x −k , x −k+1, ..., x −m , ..., x −1, x 0 are positive, has positive nonoscillatory solutions which converge to the positive equilibrium x¯ = α + 1. It is interesting that the method described in the paper, in some cases can also be applied when the parameter α is variable.