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Information × Registration Number 0225U005376, (0124U002111) , R & D reports Title New approaches and methods of the theory of boundary value problems and their application to the study of mathematical models of complex processes of support and recovery of the national economy popup.stage_title Застосування нових підходів та методів теорії крайових задач до дослідження математичних моделей комплексних процесів підтримки та відновлення національної економіки Head Olga V. Nesmelova, Доктор фізико-математичних наук Registration Date 31-12-2025 Organization Institute of Applied Mathematics and Mechanics National Academy of Science of Ukraine popup.description1 The purpose of the research work is to develop new approaches and methods for studying the properties, obtaining the conditions of solvability, constructing effective schemes for finding solutions to linear and nonlinear boundary value problems for ordinary differential, differential-algebraic, integal-differential and elliptic equations with various boundary conditions and applying them to the analysis and prediction of complex processes arising in various sectors of economic activity and industry. popup.description2 The aim of phase II of the project is to develop new approaches and methods for studying properties, obtaining solvability conditions, constructing effective schemes for finding solutions of linear and nonlinear boundary value problems for differential equations with various boundary conditions, and applying them to the analysis and modeling of complex processes that arise in the fields of economic activity and industry. The following main results were obtained: 1. We studied various cases of nonlinear boundary value problems, in particular, unsolved with respect to the derivative and problems with switching, determined the conditions for the existence of solutions and, with the use of various approaches and methods, constructed iterative schemes with accelerated convergence. The results obtained were applied to the study of mathematical models of various processes. 2. The conditions for the existence of solutions of integro-differential equations and boundary value problems for them in different spaces were determined and applied to the modelling of socio-economic processes. 3. We found Fredholm numbers and the index of one-dimensional linear boundary value problems for differential equations/systems of higher orders in spaces of smooth functions under the condition of maximum generality of the boundary operator and obtained conditions for their correct solvability, established boundary theorems for the characteristic matrices of these problems. 4. We found sufficient conditions for the regularity of solutions of elliptic boundary value problems with rough boundary data on different scales of Banach or quasi-Banach spaces of generalised functions and obtained a priori estimates of solutions. Product Description popup.authors Soldatov Vitalii O. Chepurukhina Iryna S. Ivanna A. Bondar popup.nrat_date 2025-12-31 Close