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We establish necessary and sufficient conditions for the existence of solutions to the linear boundary-value problem for a Fredholm-type matrix integrodifferential system with degenerate kernel in the critical case. We also determine the structure of generalized Green operator of this problem. [ABSTRACT FROM AUTHOR]

For a matrix differential-algebraic boundary-value problem, we establish the conditions of existence and the structure of the best (in a sense of the least-squares method) pseudosolution of this matrix differentialalgebraic boundary-value problem. [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 establish necessary and sufficient conditions for the existence of solutions of a linear periodic matrix boundary-value problem for a system of differential equations with concentrated delay in the critical case. We deduce conditions for the existence of the best solution (in a sense of the least-squares method) of the linear periodic matrix boundary-value problem for a system of differential equations with concentrated delay and find this solution. [ABSTRACT FROM AUTHOR]

We establish necessary and sufficient conditions for the existence of solutions of a linear matrix boundaryvalue problem for a system of matrix differential-algebraic equations with pulsed action. We also construct a generalized Green operator of linear boundary conditions for a system of matrix differentialalgebraic equations with pulse action. To solve the matrix differential-algebraic boundary problem with pulsed action, we use the original conditions of solvability and the structure of the general solution of the linear matrix equation. [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]

We establish constructive conditions of solvability and an algorithm for the construction of solutions of an autonomous periodic boundary-value problem for a matrix differential equation. [ABSTRACT FROM AUTHOR]

We investigate the problem of the determination of conditions for the existence of solutions of weakly nonlinear Noetherian boundary-value problems for systems of ordinary differential equations and the construction of these solutions. We consider the special critical case where the equation for finding the generating solution of a weakly nonlinear Noetherian boundary-value problem turns into an identity. We improve the classification of critical cases and construct an iterative algorithm for finding solutions of weakly nonlinear Noetherian boundary-value problems in the special critical case. [ABSTRACT FROM AUTHOR]