On a Class of Nonautonomous Max-Type Difference Equations

Abstract EN

This paper addresses the max-type difference equation xn=max{fn/xn−kα,B/xn−mβ}, n∈ℕ0, where k,m∈ℕ, B>0, and (fn)n∈ℕ0 is a positive sequence with a finite limit.

We prove that every positive solution to the equation converges to max{(limn→∞fn)1/(α+1),B1/(β+1)} under some conditions.

Explicit positive solutions to two particular cases are also presented.