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Information × Registration Number 0218U001059, 0115U003182 , R & D reports Title Constructive methods of analysis of Noetherian boundary-value problems for systems of differential, functional-differential and differential-algebraic equations and approximation theory. popup.stage_title Head Chujko Sergey Mihailovich, Registration Date 12-01-2018 Organization State Higher Educational Institution "DONBAS STATE PEDAGOGICAL UNIVERSITY popup.description2 In this research, the constructive conditions for the existence of solutions and the construction of Green's operators for linear matrix differential, functional-differential and differential-algebraic boundary-value problems were obtained. We constructed effective iterative schemes for finding solutions of matrix boundary value problems for systems of ordinary differential equations. We obtained original conditions for the existence of solutions and constructed modified iterative schemes with using least-squares technique and the Newton-Kantorovich method for nonlinear boundary value problems for systems of ordinary differential equations. Also in this research we solved some important extreme problems of the theory of approximation of functions of real and complex variables, in particular: the direct and inverse theorems of the approximation theory and the conditions of embedding on Stepanets classes in Lebesgue spaces with a variable exponent and in Orlicz spaces were found; new Bernshtein and Chebyshev type inequalities were proved; the exact values of the best approximations, the basic widht, the Kolmogorov width, the best n-term approximation in discrete Orlicz spaces are found; the properties of the operator-sieve F. Wiener are investigated. We also calculated the values of the best approximations of the Cauchy kernel on the real axis by some subspaces of spaces of sumable functions, and the conditions of convergence of Fourier series on the Takenaka-Malmquist-Dzhrbashyan systems are found. Product Description popup.authors Нєсмєлова Ольга Володимирівна Савчук Віктор Васильович Чайченко Станіслав Олегович Чуйко Олена Вікторівна popup.nrat_date 2020-04-02 Close