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Документ Application of differential equations analysing the food processes(2013) Tkachuk, Alla; Martynenko, MichailThe work is dedicated to the construction of the mathematical model of the diffusion problem which is accompanied by a chemical reaction.Документ Application of ordinary differential equations in solving diffusive problem(2013) Tkachuk, Alla; Mazur, OlehIt is investigated the changing of concentration of expanded fluid in thickness of diffusive stratum. A solution of the given problem has been received as a solution of an ordinary second-order differential equation i.e. as a solution of Cauchy problem.Документ Application of the averaging method to some optimal control problems(2013) Mogileva, Victoria; Stanzhytskyi, O.; Tkachuk, AllaAn optimal control problem for non-linear differential equations system with small parameter has been considered. To the study of such problems the application of the averaging method is justified.Документ Importance of Lyapunov's function for the existence of invariant sets of systems of differential and corresponding difference equations(2015) Tkachuk, Alla; Semenyshyna, IrinaImportant results about existence invariant sets of differential systems in terms of zeros of non-negative Lyapunov’s functions have been obtained by mathematicians.Документ Invariant Sets of Ito Stochastic Systems(2013) Stanzhytskyi, O.; Mogileva, Victoria; Tkachuk, AllaРозглянуто систему стохастичних рівнянь Іто зі сталими Вінерівськими процесами. Для неї знайдено умови, при яких множина нулів функції Ляпунова є її інваріантною множиною. Ito stochastic system with scalar Wiener processes is considered. Authors have obtained conditions when a set of zeros of Liapunov function is its invariant set.Документ The existance of positive definite Lyapunov function for the differential equations system(2007) Tkachuk, AllaThere is obtained conditions of the existence of a positive Lyapunov’s function for a system of differential equations with some properties.Документ The Existence of Liapunov's function for the invariant manifolds differential equations(2006) Tkachuk, Alla; Mogileva, VictoriaIn this work is received the result about the relation between invariant sets of systems of differential equations and the Lyapunov’s function.