Dynamics of a Rational Difference Equation

Abstract

The main goal of the paper is to investigate boundedness, invariant intervals, semicycles, and global attractivity of all nonnegative solutions of the equation , , where the parameters , is an integer, and the initial conditions . It is shown that the unique positive equilibrium of the equation is globally asymptotically stable under the condition . The result partially solves the open problem proposed by Kulenović and Ladas in work (2002).