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In this paper, we investigate the anti-periodic boundary value problem for first order impulsive delay difference equations. To begin with, we establish two comparison theorems. Then, by using these theorems, we prove the existence and uniqueness of solutions for the linear problem. Finally, by using the method of upper and lower solutions coupled with the monotone iterative technique, we obtain the new existence results of extremal solutions. Meanwhile, an example is given to illustrate the results obtained.

Anti-periodic boundary value problem for first order impulsive delay difference equations