Асташова И.В., Барабанов Е.А., Боровских А.В., Бутузов В.Ф., Быков В.В., Ветохин А.Н., Глызин С.Д., Горицкий А.Ю., Денисова Н.В., Изобов Н.А., Ильин А.В., Ильяшенко Ю.С., Капустина Т.О., Кигурадзе И.Т., Козлов В.В., Колесов А.Ю., Коньков А.А., Ломов И.С., Моисеев Е.И., Палин В.В. и др.//Дифференциальные уравнения, 2021

ОЛЕКСАНДР АНДРIЙОВИЧ БОЙЧУК (до 70-рiччя вiд дня народження) 30 червня виповнилося 70 рокiв знаному науковцю, члену-кореспонденту НАН України, лауреату Державної премiї України в галузi науки i технiки Олександру Андрiйовичу Бойчуку.Народився Олександр Андрiйович в мiстi Кiровоградi (нинi --Кропивницький).У 1967 роцi закiнчив зi срiбною медаллю Кiровоградську середню школу № 11 та вступив до Київського державного унiверситету iменi Тараса Шевченка на механiко-математичний факультет.З 1974 року навчався в аспiрантурi Iнституту математики НАН України, пiсля закiнчення якої захистив у 1978 роцi кандидатську дисертацiю

For higher-order sublinear nonautonomous ordinary differential equations, necessary and sufficient conditions for the existence of properties A and B are obtained. In particular, we prove that if n is even, a > 0, and the function p : [a, +∞) → (−∞, 0] is Lebesgue integrable on each finite interval, then, for the oscillation property of all proper solutions of the differential equation u(n) = p(t) ln(1+|u|) sgn(u), it is necessary and sufficient that \(\int_{a}^{+\infty}p(t)\rm{ln} \it{t} dt=-\infty\).

We study the existence of solutions continuously depending on a parameter for higher-order nonlinear ordinary differential equations with linear boundary conditions. In particular, we prove a theorem of Fredholm type providing tests for the unique solvability of this problem.

For second-order differential equations singular with respect to the phase variable, we obtain in a sense optimal criteria for the existence and uniqueness of positive solutions of nonlinear nonlocal boundary value problems.

For second-order linear differential equations, we obtain sharp sufficient conditions for the well-posedness of nonlocal problems with functional and multipoint boundary conditions.

For linear singular differential equations of higher order, we obtain necessary and sufficient conditions for nonlocal boundary value problems to be well posed or conditionally well posed.

For higher-order linear singular equations, we find sharp estimates for the Cauchy function and its partial derivatives. We use these estimates to study the properties of solutions of singular differential inequalities and obtain optimal sufficient conditions for the unique solvability of the linear singular Cauchy problem.

For higher order ordinary differential equations, new sufficient conditions on the existence and uniqueness of periodic solutions are established. Results obtained cover the case when the right-hand side of the equation is not of a constant sign with respect to an independent variable.

LyudmilaMikhailovna Millionshchikova (Mukhina), is the author of several books of poetry.As early as in secondary school, Vladimir Millionshchikov became interested in mathematics and studied it on his own by reading popular books; three times he won second prizes at Moscow Mathematical Olympiads.After graduating from secondary school with excellence in 1956, Millionshchikov entered the Faculty of Mechanics and Mathematics of Moscow State University at the same year, graduated from it with excellence in 1961, and began postgraduate studies under V.V. Nemytskii.During his student years, Millionshchikov began to participate in the scientific seminar held by Nemytskii, who suggested him two topics for investigation, differential equations in locally convex spaces and topological dynamics.In Millionshchikov's papers published on the first topic during his student years, he generalized a number of theorems of the theory of ordinary differential equations to the case of linear topological or locally convex spaces.In the second topic, he was the author of one of first publications on so-called nonautonomous topological dynamics.In less than two years, developing the approach used in that paper, Millionshchikov devised a method of metric (probabilistic) investigation of linear nonautonomous differential systems and constructed their metric theory.

For nonlinear nonautonomous higher-order ordinary differential equations, we prove in a sense optimal criteria for the solvability and unique solvability of a resonance periodic problem.