Global Stability of a Rational Difference Equation

الملخص EN

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).