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We establish constructive conditions for the solvability of linear boundary-value problem for a system of difference-algebraic equations and develop a scheme for the construction of solutions of this problem. We also obtain sufficient conditions for the reducibility of a difference-algebraic system to a sequence of systems combining difference and algebraic equations. We propose an original classification and a unified scheme of construction of the solutions of difference-algebraic boundary-value problems. [ABSTRACT FROM AUTHOR]

We establish constructive conditions for the solvability of a linear Noetherian boundary-value problem for a matrix difference equation and propose a procedure of construction of its solutions. We suggest an original scheme of regularization of a linear Noetherian boundary-value problem for a linear degenerate system of difference equations. [ABSTRACT FROM AUTHOR]

We found solvability conditions and a construction of the generalized Green operator for a linear matrix boundary-value problem; we present an operator that reduces a linear matrix equation to the conventional linear Noether boundary-value problem. To solve a linear matrix system, we use the operator that reduces a linear matrix equation to a linear algebraic equation with a rectangular matrix. [ABSTRACT FROM AUTHOR]