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Information × Registration Number 0221U102183, 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 28-01-2021 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 The first stage of research work was performed by the staff of the Department of Differential Equations and Oscillation Theory, including the Laboratory of Boundary Value Problems of Differential Equations Theory, 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, theory of piecewise smooth and piecewise linear mappings, dynamic and Hamiltonian systems and their applications, etc. Object of study: nonlinear systems of ordinary differential equations, functional-differential, difference, integral, operator equations and boundary-value problems for them, piecewise-smooth and piecewise-linear mappings. The purpose of the work is to make new and develop existing methods for studying solutions of wide classes of nonlinear functional-differential and impulse systems, as well as dynamic systems with discrete time. Research methods: qualitative and numerical-analytical methods of analysis of differential, functional-differential and operator equations, Lyapunov – Schmidt theory, methods of generalized inverse operators and functional analysis. The results are obtained that make a significant contribution to the development of fundamental science and meet high international standards, in particular: the theory of nonlinear boundary-value problems for differential systems and integro-differential equations, normally solvable operator equations in Banach and Hilbert spaces is 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 2021-01-28 Close