In memory of the scientist Vasil' Yukhymovych Slyusarchuk (Q6648624)

A short description of the life and scientific path of Vasil' Yukhymovych Slyusarchuk (September 24, 1946 -- February 28, 2024) is presented. V. Yu. Slyusarchuk has world-class scientific results in the field of differential equations and functional analysis. He disproved Lubich's differential mapping hypothesis, proved the density of the set of unsolvable Cauchy problems in the space of all Cauchy problems in the case of an infinite-dimensional Banach space, and the density of the set of Cauchy problems with nonunique solutions in the set of all Cauchy problems in the case of a Banach space of arbitrary dimension. He introduced the concept of essentially unstable solutions of evolutionary equations and studied equations with essentially unstable solutions, obtained new theorems about stability and instability by linear approximation of solutions of evolutionary equations. He established the necessary and sufficient conditions for the reversibility of linear non-autonomous c-continuous functional-differential operators, the necessary and sufficient conditions for the absolute stability of dynamic systems with an aftereffect; found new conditions for the existence of almost periodic solutions of nonlinear differential, difference, differential-difference, and functional equations. He obtained general results on the convergence of numerical series, special cases of which are the corresponding classical results. Proposed a new mathematical model of the solar system taking into account the finite speed of gravity and proved the non-Keplerianism and instability of the motion of two bodies caused by the finite speed of gravity. See, for example, [\textit{V. Yu. Slyusarchuk}, J. Math. Sci., New York 278, No. 6, 1092--1101 (2024; Zbl 1533.39004); [ J. Math. Sci., New York 277, No. 2, 329--337 (2023; Zbl 1533.70010)]; [J. Math. Sci., New York 273, No. 2, 290--315 (2023; Zbl 1531.83011)]; [J. Math. Sci., New York 270, No. 2, 353--384 (2023; Zbl 1531.70021)]; [ J. Math. Sci., New York 263, No. 2, 299--326 (2022; Zbl 1508.70013)]; [ J. Math. Sci., New York 243, No. 3, 467--492 (2019; Zbl 1456.70024)]; [ J. Math. Sci., New York 243, No. 2, 287--312 (2019; Zbl 1455.70014)].