Copyright © 2010 Wanping Liu and Xiaofan Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper studies the behavior of positive solutions to the following particular case of a difference equation by Stević xn+1=A+xnp/xn−kpk+1, n∈ℕ0, where A,p∈(0,+∞), k∈ℕ, and presents theoretically computable explicit lower and upper bounds for the positive solutions to this equation. Besides, a concrete example is given to show the computing approaches which are effective for small parameters. Some analogous results are also established for the corresponding Stević max-type difference equation.