Abstract
We consider the higher‐order nonlinear difference equation xn+1 = (p + qxn−k)/(1 + xn + rxn−k), n = 0, 1, … with the parameters, and the initial conditions x−k, …, x0 are nonnegative real numbers. We investigate the periodic character, invariant intervals, and the global asymptotic stability of all positive solutions of the above‐mentioned equation. In particular, our results solve the open problem introduced by Kulenović and Ladas in their monograph (see Kulenović and Ladas, 2002).
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