Global attractivity of the equilibrium of a difference equation: An elementary proof assisted by computer algebra system

摘要

Let p and q be arbitrary positive numbers. It is shown that if q < p, then all solutions to the difference equation X_(n+1) = p + qx_n/1 + X_(n-1), n = 0, 1, 2,..., X_(-1) > 0, X0 > 0 (E) converge to the positive equilibrium,. The above result, taken together with the 1993 result of Koci? and Ladas for equation (E) with q ≥ p, gives global attractivity of the positive equilibrium of (E) for all positive values of the parameters, thus completing the proof of a conjecture of Ladas.