On a class ofnonautonomous max-type difference equations

Abstract

This paper addresses the max-type difference equation xn = max {fn / xαn-k, Bβ/ x n-m }, n ε ℕ0, where k, mε ℕ , B>0, and (fn)ε ℕ0 is a positive sequence with a finite limit. We prove that every positive solution to the equation converges to max { (lim n → ∞ fn)1/(α+1), B 1/ (β+ 1)} under some conditions. Explicit positive solutions to two particular cases are also presented.