On a Class of Nonautonomous Max-Type Difference Equations

Abstract

This paper addresses the max-type difference equationxn=max{fn/xn−kα,B/xn−mβ},n∈ℕ0, wherek,m∈ℕ,B>0, and(fn)n∈ℕ0is a positive sequence with a finite limit. We prove that every positive solution to the equation converges tomax{(limn→∞fn)1/(α+1),B1/(β+1)}under some conditions. Explicit positive solutions to two particular cases are also presented.