On the max-type equation xn+1 = max {An/x n, xn-1}

Abstract

It is shown that every well-defined solution to the second-order difference equation in the title, when (An)n∈ 0 is a two-periodic sequence such that max{A0, A1} ≥ 0, is eventually periodic with period two. In the case max{A0, A 1} < 0 it is shown the existence of unbounded solutions, by describing all solutions in terms of A0, A1,x-1 and x0.