THE BOUNDEDNESS OF NON-AUTONOMOUS NONLINEAR TIME-VARYING DELAY DIFFERENCE EQUATIONS SUBJECT TO EXTERNAL DISTURBANCES an‎d ITS APPLICATIONS

First, we employ fixed point theory and compute some difference inequalities to derive some new results on the existence of positive solutions and the equi-boundedness of solutions. Second, we derive a sufficient condition for the ultimate boundedness of solutions. Third, we apply the obtained results to some discrete population models. Finally, numerical examples are given to illustrate the effectiveness of the proposed results.