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Information × Registration Number 0218U001920, 0118U003390 , R & D reports Title The constructive methods of analysis of matrix boundary value problems for the ordinary systems of differential, algebraic-differential and functional-differential equations and the theory of approximation. popup.stage_title Head Chujko Sergey Mihailovich, Registration Date 21-12-2018 Organization State Higher Educational Institution "DONBAS STATE PEDAGOGICAL UNIVERSITY popup.description2 In the course of the study, the solvability conditions were found, as well as the construction of a generalized Green operator of a linear matrix boundary value problem in a Banach space; the solvability conditions and the construction of a generalized Green operator for the Cauchy problem for a linear differential algebraic system were found; the original classification, as well as a unified scheme for constructing solutions of differential-algebraic equations is proposed; the existence conditions for the matrix differential-algebraic boundary value problem were found, as well as the construction of the best (in the sense of the smallest squares) pseudo-solution of the matrix differential-algebraic boundary value problem; the conditions of existence and image of the best (in the sense of the least squares method) solution of the linear matrix periodic problem for a system of differential equations with a lagged delay were obtained; the problem of finding the conditions of existence and construction of solutions of a linear noetherian boundary value problem for a hybrid system of ordinary differential equations and difference equations was investigated; the algorithm for constructing solutions of a linear noetherian boundary-value problem for a hybrid system of differential-difference equations in a critical and noncritical case is proposed; an improved scheme for the study of autonomous noetherian boundary value problems for nonlinear systems in critical cases is proposed. Also, investigations of extremal problems on the best rational approximations with the help of Fourier series in the Takenaki-Malmquist system in a unit circle were continued; the exact values of the best rational approximations of Bergman weigth kernels on the unit circle of the complex plane in quadratic and uniform metrics were calculated; two identities were proved which associate the coefficients of Faber polynomials with the coefficients of the Laurent layouts of the corresponding conformal mappings; the values of the best approximations were calculated on the average on a unit circle of the Cauchy Segjo kernel using quasipolynoms in the Takenaki-Malmquist system; an extremal problem is solved about finding the exact values of the best linear approximation of the class of functions represented by integrals of the Cauchy-Stilltiess type and the construction of the best linear approximation method in such a class. Product Description popup.authors Дзюба Марина Володимирівна Нєсмєлова Ольга Володимирівна Савчук Віктор Васильович Сисоєв Денис Віталійович Чайченко Станіслав Олегович Чуйко Олена Вікторівна popup.nrat_date 2020-04-02 Close