On Some Properties of Solutions of Systems of Linear Difference Equations with Periodic Right-Hand Sides

Abstract

We consider homogeneous and inhomogeneous systems of linear difference equations with coefficients that are-periodic functions of discrete time. For homogeneous systems, sufficient conditions for the existence of periodic and almost periodic solutions are obtained. For inhomogeneous systems, it is shown that a necessary and sufficient condition for the existence of an N-periodic solution is the existence of a bounded solution. Necessary and sufficient conditions for theN orthogonality of the fundamental matrix of the homogeneous system are established. Illustrative examples are given.