Global attractivity of a higher order nonlinear difference equation

In this paper the global attractivity of the nonlinear difference equation y(n+1) = p + qyn/1 + yn + ryn-k, n = 0, 1, ..., is investigated, where p , q , r is an element of [0, infinity), 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).