On the difference equation x n = a nx n-k/(b n + c nx n-1⋯x n-k)

Abstract

The behavior of well-defined solutions of the difference equation x n = a nx n-k/(b n + c nx n-1⋯x n-k), n ∈ ℕ 0, where k ∈ ℕ is fixed, the sequences a n, b n and c n are real, (b n, c n) ≠ (0,0), n ∈ ℕ 0, and the initial values x -k, ⋯, x -1 are real numbers, is described. © 2012 Stevo Stević et al.