Abstract
In this paper, we study the boundedness, the invariant intervals,the periodic character and the global asymptotic stability of all positive solutions of the higher order nonlinear difference equation yn+1=p+qyn−k1+yn−k+ryn−k−1,n=0,1,…, where the parameters p,q,r∈(0,∞),k∈{0,1,2,…}, and the initial conditions y−k−1,y−k,…y0∈[0,∞). We show that the unique positive equilibrium of the above equation is globally asymptotically stable under certain conditions.
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