On a class of nonautonomous max-type difference equations (Q638121)

Summary: This paper addresses the max-type difference equation \(x_n = \max \{f_n/x^{\alpha}_{n-k}, B/x^{\beta}_{n-m}\}\), \(n \in \mathbb N_0\), where \(k, m \in \mathbb N\), \(B > 0\), and \((f_n)_{n\in \mathbb N_0}\) is a positive sequence with a finite limit. We prove that every positive solution to the equation converges to \(\max\{(\lim_{n \rightarrow \infty}f_n)^{1/(\alpha +1)}, B^{1/(\beta +1)}\}\) under some conditions. Explicit positive solutions to two particular cases are also presented.