$\boldsymbol{Ψ}$-Bounded Solutions for a System of Difference Equations on $\mathbb{Z}$

Abstract

In this work we discuss the existence of $\boldsymbol{Ψ}$-bounded solutions for linear difference equations. We present a necessary and sufficient condition for the existence of $\boldsymbol{Ψ}$-bounded solutions for the linear nonhomogeneous difference equation $\boldsymbol{x}(n+1) = \boldsymbol{A}(n) \boldsymbol{x}(n) + \boldsymbol{f}(n)$ for every $\boldsymbol{Ψ}$-bounded sequence $\boldsymbol{f}(n)$.