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Information × Registration Number 0222U000957, 0120U100180 , R & D reports Title Numerical-analytical methods of the theory of nonlinear oscillations, functional-differential and impulsive systems popup.stage_title Head Boichuk Oleksandr A., Доктор фізико-математичних наук Registration Date 22-01-2022 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 Research work "Numerical-analytical methods of the theory of nonlinear oscillations, functional-differential and impulsive systems" was performed by the staff of the Department of Differential Equations and Oscillation Theory, including the Laboratory of Boundary Value Problems of Differential Equations, during the reporting period in the following areas: normally solvable boundary-value problems for operator, differential and integral equations, qualitative methods of the theory of nonlinear oscillations, the theory of piecewise smooth and piecewise linear mappings, dynamical and Hamiltonian systems and their applications, etc. Object of research: nonlinear systems of ordinary differential equations, functional-differential, difference, integral, operator equations and boundary value problems for them, piecewise-smooth and piecewise-linear mappings, shape-preserving approximation. The aim of the work is to study evolutionary problems that simulate various phenomena of nonlinear, including purely oscillatory, nature, development of new and development of existing methods for studying solutions of broad classes of nonlinear functional-differential and impulse systems, and dynamic systems with discrete time. Research methods: qualitative and numerical-analytical methods of analysis of differential, functional-differential and operator equations, Lyapunov–Schmidt theory, the apparatus of generalized inverse operators, methods of functional analysis. The results that made a significant contribution to the development of basic science and meet high international standards, in particular: the theory of nonlinear boundary-value problems for systems of integro-differential equations, normally solvable operator equations in Banach and Hilbert spaces was developed; qualitative and analytical methods of the theory of nonlinear oscillations are developed; the solvability of systems of mathematical physics, bifurcation transitions in oscillatory networks are investigated. Product Description popup.authors popup.nrat_date 2022-03-09 Close