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Information × Registration Number 0220U102879, 0115U001308 , R & D reports Title Researching of solutions of the linear and nonlinear differential equations and its systems and integro-differential equations of mathematical physics popup.stage_title Head Shchoholev Serhii A, Registration Date 16-06-2020 Organization Odessa I.I.Mechnikov National University popup.description2 The object of the study is finite-dimensional linear and quasi-linear differential equations and their systems. Countable systems of differential equations. Integro-differential equations of mathematical physics and boundary value problems of the theory of analytic functions. The purpose of the work is to create a conceptual basis for the method of research of finite-dimensional and countable systems of linear and quasi-linear differential equations with oscillatory type coefficients with slowly varying parameters, as well as methods for researching the asymptotic behavior of solutions of essentially nonlinear systems of differential equations and systems of differential equations, including solutions of the boundary value problems of the theory of analytic functions. During the study, the methods of differential and integral calculus, qualitative and analytical theory of differential equations, linear algebra (in particular, matrix theory) and functional analysis (in particular, the principle of contraction mappings) were used. The study was conducted in several main areas: 1. For finite-dimensional and countable linear and nonlinear systems differential equations with coefficients depicted as Fourier series with slowly varying parameters, establishing the conditions for the existence of solutions of the same type. Establishment of signs of possibility of splitting linear systems of differential equations with oscillatory coefficients into subsystems of smaller dimensions. Indication of the possibility of reducing such systems to systems with slowly variable coefficients. 3. Establishment of new conditions of existence and construction of asymptotic at development of solutions of nonlinear systems of differential equations. 3. Establish new conditions of existence and construct asymptotic ones for development of monotonic solutions of nonlinear 2nd order nonlinear differential equations. 4. Establish sufficient conditions for resolution of the Riemann  Product Description popup.authors Dzhashitova Vira V Dzhashitova Vira V Drick Natalya G Drick Natalya G Kerekesha Denis P Kerekesha Denis P Koltsova Liliia L Koltsova Lilia L Korenovskyi Arkadii O Korenovsky Arkadiy O popup.nrat_date 2020-07-03 Close