On a difference equation with min‐max response

Abstract

We investigate the global behavior of the (positive) solutions of the difference equation

Boundedness character of positive solutions of a higher order difference equation

“…The behaviour of solutions of Equation (1) and its generalizations has been investigated for some time, see [1-10,12-16,21-25, [27][28][29][30][31] and the references therein. If k is even, m is odd and A ∈ (0, 1), then Equation (1) has unbounded solutions [19]. In a talk [24], the third author posed the following conjecture.…”