On periodic solutions of systems of linear finite-difference equations in the critical case (Q946135)

The author studies the system of linear finite-difference equations \[ x(t+1)=A(t)x(t)+F(t),\tag{1} \] where \(t\in \mathbb{R}^{+}= [0,+\infty),\) \(A(t)\) is a real \(n\times n\) matrix, \(F(t)\) is a real \(n\)-vector, and \(x(t)\) is an unknown \(n\)-vector function. Sufficient conditions for the existence and a method for the construction of periodic solutions of system (1) in the critical case are obtained.