In 1963, after the graduation from the postgraduate courses at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR, Samoilenko defended his candidate-degree thesis "Application of Asymptotic Methods to the Investigation of Nonlinear Differential Equations with Irregular Right-Hand Side" and began his work at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR under the supervision of Academician Yu.
[citation needed] In 1965–1974, 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.
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.
[2] 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.
Based on results of the research in the theory of differential equations with delay performed at that time, the monograph[3] of Mitropolskiy, Samoilenko, and D. I. Martynyuk was published.
The beginning of this fruitful creative period was marked by the fundamental monograph[8] 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 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.
[11][12][13][14] 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.
The monographs [19][20] of Samoilenko and R. I. Petryshyn cover a broad class of qualitative problems in the theory of nonlinear dynamical systems on a torus.
Many young talents from the "small homeland" of Samoilenko (Malynshchyna) are grateful to him for founding and heading the charity foundation for support of the development of gifted children and youth.
For example, Samoilenko's alma mater (the Department of Mechanics and Mathematics at the Shevchenko Kyiv National University) has been headed for many years by his disciples (Professors M. O. Perestyuk and I. O. Parasyuk).