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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 971394, 5 pages
http://dx.doi.org/10.1155/2013/971394
Research Article

On Linear Difference Equations for Which the Global Periodicity Implies the Existence of an Equilibrium

Department of Mathematics, University of Pannonia, Egyetem Utca 10, Veszprém 8200, Hungary

Received 5 September 2013; Revised 4 November 2013; Accepted 18 November 2013

Academic Editor: Agacik Zafer

Copyright © 2013 István Győri and László Horváth. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It is proved that any first-order globally periodic linear inhomogeneous autonomous difference equation defined by a linear operator with closed range in a Banach space has an equilibrium. This result is extended for higher order linear inhomogeneous system in a real or complex Euclidean space. The work was highly motivated by the early works of Smith (1934, 1941) and the papers of Kister (1961) and Bas (2011).