There is used a version of Schauder’s fixed point theorem to prove the existence of asymptotically periodic solutions of a scalar Volterra difference equation. Along with the existence of asymptotically periodic solutions, sufficient conditions for the nonexistence of such solutions are derived. Results are illustrated on examples.
© 2012 Josef Diblík, Miroslava Růžičková, Ewa Schmeidel, published by Slovak Academy of Sciences, Mathematical Institute
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