Abstract
In this paper the global attractivity of the nonlinear difference equation is investigated, where p, q, r ∈ [0, ∞), k ≥ 1 is a positive integer and the initial conditions y − k ,…,y − 1 are nonnegative real numbers and y 0 is a positive real number. We show that the unique positive equilibrium of the equation is a global attractor. In particular, our results solve the open problem proposed by Kulenovic and Ladas in their monograph (Dynamics of Second Order Rational Difference Equations: with Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, 2001).
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