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).
"On Linear Difference Equations for Which the Global Periodicity Implies the Existence of an Equilibrium." Abstr. Appl. Anal. 2013 (SI28) 1 - 5, 2013. https://doi.org/10.1155/2013/971394