On a generalized max-type difference equation from automatic control theory

Abstract

This paper studies the boundedness character of positive solutions of the following generalization of a max-type difference equation from automatic control theory (see, Mishkis, (1977) [18] and Popov (1966) [21]) xn + 1 = max {A, frac(underover(x, n, p), underover(x, n - 1, q) xn - 2r)}, n ∈ N0, where the parameters A, p, q and r are positive numbers. In the study of the equation we also introduce a new method called Oachkatzlschwoif.