Global stability of yn+1=p+qyn+ryn-k1+yn

In this paper, we investigate the global stability of difference equation,yn+1=p+qyn+ryn-k1+yn,n=0,1,2,…,where the initial conditions y−k, … , y−1, y0 are non-negative, k ∈ {1, 2, 3, …}, and the parameters p, q and r are non-negative. We show that when r < q + 1, then the unique positive equilibrium of this equation is globally asymptotically stable and when r > q + 1, and k is odd, then this equation possesses unbounded solutions.