$\boldsymbol{Ψ}$-Bounded Solutions for a System of Difference Equations on $\mathbb{Z}$ (Communications in Mathematical Research, 2021)
In this work we discuss the existence of $\boldsymbol{Ψ}$-bounded solutions for lineardifference equations. We present a necessary and sufficient condition for the existenceof $\boldsymbol{Ψ}$-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 $\boldsymbol{f}(n)$.