Between 1965–74, Samoilenko worked as a senior research fellow at the
Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR and gave lectures at the
Shevchenko Kyiv State University. In 1974, he obtained the
professor degree. In 1978, he was elected to become a
Corresponding Member of the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR. His monograph brought him worldwide recognition. This monograph was written by Samoilenko together with his teachers, Academicians
N. N. Bogolyubov and Yurii Mitropolskii. 36 years later, Samoilenko reminisced, "In Kyiv, at the Institute of Mathematics, great scientists were my teachers... In many fields of science, they were 'trendsetters' on the scale of the Soviet Union. It is very important for a young scientist to belong to a serious scientific school. Probably, only in this case he has a chance to obtain results at the world level. The atmosphere of a good scientific school itself stimulates a young scientist to carry out his research work at the cutting edge of modern science. And if he suddenly opens a new direction in science, then his name immediately gains recognition". In 1974–1987, Samoilenko headed the Chair of Integral and
Differential Equations of the Department of Mechanics and Mathematics at the
Shevchenko Kyiv State University. These years were marked by especially high scientific activity of the chair. Based on results of the research in the theory of differential equations with delay performed at that time, the monograph of
Mitropolskiy, Samoilenko, and
D. I. Martynyuk was published. At the same time, Samoilenko, together with his disciple
M. O. Perestyuk, published the well-known monograph devoted to the theory of impulsive differential equations. These monographs (especially their English translations) are frequently cited in scientific literature. Since 1987, Samoilenko has headed the Department of Ordinary Differential Equations at the
Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR (at present, the Department of Differential Equations and Theory of Oscillations at the
Institute of Mathematics of the National Academy of Sciences of Ukraine), and since 1988 he has been the Director of the Institute of Mathematics of the National Academy of Sciences of Ukraine. The beginning of this fruitful creative period was marked by the fundamental monograph devoted to the qualitative theory of invariant manifolds of dynamical systems. This monograph served as a foundation for the construction of the general
perturbation theory of
invariant tori of nonlinear
dynamical systems on a
torus. The English version of this monograph is also well known. Three years later, the monograph of Samoilenko (in coauthorship with Mitropol'skii and
V. L. Kulyk) was published. In this monograph, in particular, the method of
Lyapunov functions was used for the investigation of
dichotomies in linear differential systems of the general form. The results of many-year investigations of constructive methods in the theory of
boundary-valued problems for ordinary differential equations carried out by Samoilenko together with
M. Ronto are presented in monographs. Constructive algorithms for finding solutions of boundary-value problems with different classes of multipoint boundary conditions were developed by Samoilenko,
V. M. Laptyns'kyi, and
K. Kenzhebaev; the obtained results are presented in monograph. Complex classes of
resonance boundary-value problems whose linear pan cannot be described by
Fredholm operators of index zero were investigated by Samoilenko, together with
O. A. Boichuk and
V. F. Zhuravlev, in monographs. The monograph of Samoilenko and
Yu. V. Teplins'kyi is devoted to the theory of
countable systems of ordinary differential equations. The monographs of Samoilenko and
R. I. Petryshyn cover a broad class of qualitative problems in the theory of nonlinear dynamical systems on a torus. ==Work==