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Information × Registration Number 0220U100845, 0116U003121 , R & D reports Title Constructive and qualitative methods of analysis of differential, functional-differential, impulsive and difference equations popup.stage_title Head Samoilenko Anatoly M., Доктор фізико-математичних наук Registration Date 28-01-2020 Organization The Institute of Mathematics of NASU popup.description2 The 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 nonlinear oscillations theory, theory of piece-smooth and piece-linear mappings, dynamic and Hamiltonian systems and their applications. Object of study: nonlinear systems of ordinary differential and impulsive equations, functional-differential, difference, integral, operator equations and boundary value problems for them, piece-smooth and piece-linear mappings. The purpose of the work is to study evolutionary models that describe various physical phenomena of nonlinear character, to develop new ones and to improve the existing methods of investigating the solutions of nonlinear differential and functional differential equations, impulse and difference equations. Research methods: qualitative and numerical-analytical methods of analysis of differential, functional-differential and operator equations, Lyapunov–Schmidt theory and apparatus of generalized inverse operators. The obtained results make a significant contribution to the development of fundamental science and satisfy high level international standards, in particular: the general concept of the study of nonlinear boundary value problems for differential systems with delay, equations with impulsive action, integro-differential equations, normally solvable operator equations in Banach and Hilbert spaces; qualitative and analytical methods of the theory of nonlinear oscillations; almost periodic evolution systems with state-dependent impulses and bifurcation transitions in coupled-phase oscillator systems. Product Description popup.authors popup.nrat_date 2020-04-02 Close