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Existence of asymptotically periodic solutions of scalar Volterra difference equations. (English) Zbl 1212.39020

The existence of asymptotically periodic solutions of a scalar Volterra difference equation is discussed by using Schauder’s fixed point theorem. In addition, a concrete example is illustrated to show the usefulness of the main theorem. Moreover, sufficient conditions for the nonexistence of such solutions are given.

MSC:

39A23 Periodic solutions of difference equations
39A10 Additive difference equations
39A22 Growth, boundedness, comparison of solutions to difference equations
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