Anatoly Samoilenko : biography

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 monographA. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations. Invariant Tori [in Russian], Moscow, Nauka (1987). 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 versionA. M. Samoilenko, Elements of the Mathematical Theory of Multi-Frequency Oscillations, Kluwer, Dordrecht (1991). of this monograph is also well known. Three years later, the monographYu. A. Mitropol’skii, A. M. Samoilenko, and V. L. Kulik, Investigation of Dichotomy of Linear Systems of Differential Equations Using Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1990). 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.A. M. Samoilenko and N. I. Ronto, Numerical-Analytic Methods in the Theory of Boundary-Value Problems for Ordinary Differential Equations [in Russian], Naukova Dumka, Kiev (1992).A. M. Samoilenko and N. I. Ronto, Numerical-Analytic Methods for the Investigation of Solutions of Boundary-Value Problems [in Russian], Naukova Dumka, Kiev (1986).A. M. Samoilenko and N. I. Ronto, Numerical-Analytic Methods for the Investigation of Periodic Solutions [in Russian], Vyshcha Shkola, Kiev (1976).M. Ronto and A. Samoilenko, Numerical-Analytic Methods in the Theory of Boundary-Value Problems, World Scientific, River Edge, NJ (2000). 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.A. M. Samoilenko, V. N. Laptinskii, and K. K. Kenzhebaev, Constructive Methods for the Investigation of Solutions of Periodic and Multipoint Boundary-Value Problems [in Russian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (1999). 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.A. A. Boichuk, V. F. Zhuravlev, and A. M. Samoilenko, Generalized Inverse Operators and Noetherian Boundary-Value Problems [in Russian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (1995).A. A. Boichuk and A. M. Samoilenko, Generalized Inverse Operators and Fredholm Boundary-Value Problems, VSP, Utrecht (2004). The monographA. M. Samoilenko and Yu. V. Teplinskii, Countable Systems of Differential Equations, VSP, Utrecht (2003). of Samoilenko and Yu. V. Teplins’kyi is devoted to the theory of countable systems of ordinary differential equations. The monographs A. M. Samoilenko and R. I. Petryshyn, Multifrequency Oscillations of Nonlinear Systems [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (1998).A. M. Samoilenko and R. I. Petryshyn, Mathematical Aspects of the Theory of Nonlinear Oscillations [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2004). of Samoilenko and R. I. Petryshyn cover a broad class of qualitative problems in the theory of nonlinear dynamical systems on a torus.