On a nonautonomous difference equation with bounded coefficient (Q860926)

This article deals with the nonautonomous difference equation \[ x_{n+1} = p_n + x_{n-k}\sum_{j=0}^{k-1}\frac{1}{x_{n-j}} \] of order \((k+1)\), where \(p_n\) is positive and bounded and the initial values are positive real numbers. It is a continuation of former studies, where the cases \(k = 1\) or \(p_n\) is constant, respectively, have been considered. The authors prove results for the boundedness, persistence and existence of periodic solutions and the attractivity of positive solutions.