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Information × Registration Number 0222U003410, 0119U100334 , R & D reports Title Development of new analytic-geometric, asymptotic and qualitative methods for investigating invariant sets of divergent-objective equations. popup.stage_title Head Perestiuk Mykola O., Доктор фізико-математичних наук Registration Date 20-03-2022 Organization Taras Shevchenko National University of Kyiv popup.description2 Object of research: dynamic and parabolic systems; systems of nonlinear dynamics and multifrequency oscillations; different classes of impulse systems, systems of differential equations; algebraic and topological systems. Purpose: to create new effective analytical and geometric algorithms for the study of current problems of modern theory of nonlinear evolutionary, stochastic, impulse systems, as well as algebraic systems, to obtain basic theoretical and practical statements. Research methods: theoretical analytical-geometric analysis of nonlinear systems, methods of normal forms, integral varieties, global attractors, methods of differential geometry and categorical-algebraic. The conditions for the existence of bounded solutions for the class of differential equations with continuous and momentum perturbations of the coefficients are established. The conditions for the existence of a uniform attractor for wide classes of impulse perturbations are established. The stability property of the nonpulse part of a uniform attractor for parabolic and hyperbolic weakly nonlinear impulse-perturbed infinite-dimensional evolutionary systems is proved. Sufficient conditions for the existence of bounded solutions of a weakly nonlinear multidimensional system of differential equations with impulse action are obtained. The geometric theory of the asymptotic phase is developed to describe the behavior of trajectories attracted by invariant varieties. The problem of the existence of an invariant section is reduced to the problem of establishing a fixed point of a nonlinear operator in the space of Lipschitz sections. For Fredholm-type equations, the question of the existence of global solutions, their continuous dependence on the initial data is studied, and the method of averaging is substantiated. Product Description popup.authors Asrorov Farkhod A. Vasylyk Olha I. Holovashchuk Nataliia S. Kapustyan Oleksiy V. Kushnirenko Svitlana V. Melnyk Taras A. Parasyuk Ihor O. Stanzhytskyi Oleksandr M. popup.nrat_date 2022-03-20 Close