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History

Formation of personnel of future Department of integral and differential equations began in late 1944. Officially it appears in the 1945 - 1946 academic year under the title "Department of integrating differential equations." The first of its faculty members were professors and G.V.Pfeiffer Y.Z.Shtokalo, docents K.Ya.Latysheva and L.M.Gratsianska, senior lecturer F.S.Gudymenko.

Lead for the department was entrusted to Academician of the AS USSR, a member of Moscow, Berlin and French Mathematical Society G.V.Pfeiffer (1872 - 1946). The main results of his research concerned the development of general methods of integrating differential equations with partial derivatives.

G.V.Pfeyffers successor as head in 1946 became Y.Z. Shtokalo (1897 - 1987). He started a career at Kiev University in December 1944. Y.Z.Shtokalo was a head of Department until December 1970 with a break in 1952 - 1956's, when he worked in Lviv as chairman of the Presidium of the AS USSR institutions.

Scientific direction concerned with analytical theory of differential equations within Department was initiated in 1946 by K.Ya. Latysheva (1897 - 1956) a student of Academician M.P.Kravchuk. From 1953 to 1956 he headed the Department of differential equations. She was the first among female mathematicians from Ukraine who was awarded the title of professor. From 1952 to 1954 K.Ya.Latyshev served as Dean of the Faculty of Mechanics and Mathematics.

The direction associated with the development of mathematical methods of the theory of nonlinear oscillations began to develop rapidly shortly after in 1949 there began a teaching activity Yuri Mitropol'skii (1917 - 2008).

Academician of NAS of Ukraine and the Russian Academy of Sciences Yuri Mitropol'skii is considered one of the founders of the world-famous Kiev school of nonlinear mechanics. His main results concern the algorithms for constructing asymptotic expansions of solutions of nonlinear differential equations that describe the unsteady oscillating processes, development of one-frequency method in the study of systems with many degrees of freedom, the averaging method and the method of integral manifolds.

A student of Academician Yu.O.Mitropolskii, Boris Moseyenkov (born on 18.02.1922 ) received a number of important results in the theory of oscillations of systems with distributed parameters. For such systems he studied the unsteady vibrational modes, and interesting phenomena that occur during the passage through resonance. Docent B.I.Moseyenkov worked an the Department for about forty years. From March to September 1960 and from December 1970 to October 1974 he served as its head.

In 1967, D.I.Martynyuk (1942 - 1996) began his teaching and research work at the Department. Here he rose from assistant to full professor. From 1979 to 1983 he served as Deputy Head of Department of integral and differential equations in science.

From 1988 to 1995 D.I.Martynyuk headed the Department of Mathematical Physics of the Faculty of Mechanics and Mathematics. In 1995, he leaved the position of the head of the Department of mathematical physics and returned to the Department of integral and differential equations, where he worked till the last day of his life the 27-th of October 1996. D.I.Martynyuk worked at the Faculty of Mechanics and Mathematics for more than 29 years.

The new stage of development of the Department of integral and differential equations started in 1974, when it was headed by Professor Anatoly Samoilenko a student of M.M.Bogolyubov and Yu.O.Mytropolskii.

From 1963 to 1974 A.M.Samoilenko worked at the Institute of Mathematics, first as a junior, and from 1965 - senior researcher, in 1974 - 1987 he was a head of Integral and differential equations Department of the Kiev State University. In 1987 he returned to the Institute of Mathematics of NAS of Ukraine and heads the ordinary differential equations department. A year after he was elected the Director of the Institute. In 1978 Anatoly Mikhailovich was elected a corresponding member and in 1995 - a member of the National Academy of Sciences of Ukraine. Since 2006 A.M.Samoilenko is an academician-secretary of Department of Mathematics of NAS of Ukraine.

His research interests cover many difficult problems of qualitative theory of differential equations and nonlinear mechanics. In collaboration with Yu.O.Mytropolskii he conducted an extensive research on current problems in the theory of nonlinear multi-frequency oscillations.

M. Ronto, a student of A.M.Samoilenko, dedicated nearly 10 years to the work at the department.

M.Ronto is a well-known expert in the theory of nonlinear boundary value problems. He has authored more than 160 scientific papers, including 5 monographs.

On January 15, 1987 the department was headed by Mykola Perestyuk, a student of Academician A.M.Samoilneko. As a scientist, M. Perestyuk grew up in the world-famous Krylov-Bogolyubov-Mitropol'skii Kiev school of nonlinear mechanics. His teacher, academician A.M.Samoilenko, is an outstanding mathematician of our days. Under his supervision M.Perestyuk defended in January 1972 a PhD thesis "Some question of the study of nonlinear systems of differential equations with instant changes."

In the research of young scientist a central place occupy the questions of the theory of impulsive systems and the theory of invariant sets of differential and difference equations. In the 70's and early 80-ies with A.M.Samoilenko he received the results of a priority nature, related to the existence of periodic solutions of nonlinear impulsive systems, justification of the averaging method and finding stability conditions for such systems. In fact, a new direction in the theory of ordinary differential equations has been establishing at that time. Later M.O.Perestyuk achieved significant progress in developing the theory of almost periodic solutions and the theory of integral sets for impulsive systems.

In February 1986, M.O.Perestyuk defended Dr.Sci. dissertation "Oscillating solutions of impulsive differential equations and their stability". In 1987 the book "Differential equations with impulsive perturbations", written in collaboration with A.M.Samoilenko was published. It was one of the world's first books devoted to a systematic exposition of the theory of impulsive systems. In 1995, the extended English version of the book "Impulsive differential equations" was published.

More than 20 Ph.Ds and 6 Dr.Sci were defended under the supervision of M.O.Perestyuk. His students work successfully not only in Ukraine but also in other countries: U.S., Uzbekistan, Kazakhstan, Turkmenistan, Turkey, Tajikistan, Iraq. He is an Honorary Doctor of Uzhgorod National University (2005) and Chernivtsi National University (2010).

I.O.Parasyuk was born January 18, 1953 in Lviv. He graduated from the Faculty Mechanics and Mathematics Kyiv State University (1975). From 1978 he works at the Department of integral and differential equation as assistant (1978 - 1986), docent (1986 - 1991, 1994 - 1996), Professor (since 1996).

In his doctoral thesis "Coisotropic invariant tori of Hamiltonian systems" (1995) he found and described a new type of multi-frequency nonlinear oscillations in Hamiltonian systems - Quasiperiodic motions on coisotropic invariant tori. For such movements, he developed an informal perturbation theory, which is the development of well-known theory of Kolmogorov - Arnold - Moser.

From 2003 to 2007 I.O.Parasyuk served as Dean of the Faculty of Mechanics and Mathematics of Taras Shevchenko National University of Kyiv.

O.M. Stanzhytskiy, another student of A.M.Samoilenko, began his pedagogical activity at the Department. In 1989 he defended his PhD thesis "Oscillating properties of solutions of differential equations with random perturbations." In his subsequent research he found sufficient conditions for existence and stability of periodic modes in systems in standard Bogolyubov form with the presence of periodic random (in the sense of finite-dimensional distributions) process. Later O.M.Stanzhytskiy received a number of sufficient conditions for existence of invariant sets of systems of differential equations, experiencing small random perturbations, and examined the stability of such sets, effectively applying for this a method of Lyapunov functions and reduction principle. In 2002, O.M.Stanzhytskiy successfully defended his Dr.Sci. dissertation "Qualitative analysis of differential equations with random perturbations" and later headed the Department of general mathematics.

V. S. Melnik (1953 - 2007), a gifted mathematician and cybernetics, Doctor of Sciences, corresponding member of NAS of Ukraine, worked at the Department for more than 10 years (from 1997 to 2007).

He has a number of fundamental results on the theory of multivalued dynamical systems in infinite dimensional spaces, nonlinear analysis, equations in partial derivatives, theory of optimal control in Banach spaces. He laid the foundations of the theory multi-dynamical systems in Banach and topological spaces, introduced multivalued semiflows (multivalued analogue of one-parameter semigroups of operators) and examined the structure of their global attractors. For the first time, it enables to solve the problem of qualitative analysis of differential-operator inclusions and evolution equations without uniqueness of solutions.

O.A. Boichuk, a student of A.M.Samoilenko, are working at the Department for more than 12 years. After the graduation from Taras Shevchenko University of Kyiv, he works at the Institute of Mathematics of NAS of Ukraine, where under supervision of A.M.Samoilenko he received a number of outstanding results in the theory of Noetherian boundary problems, which formed the basis for his Dr.Sci. dissertation (1992). In 1997 he received the title of professor in the specialty "differential equation". In 2004, together with his teacher A.M.Samoilenko, he published a monograph "Generalized Inverse Operators and Fredholm Boundary Value Problems

O.V. Kapustyan has been working at the Department since 1999. He was born on October 30, 1975 in Dnepropetrovsk. After graduating with honors from the Faculty of Mechanics and Mathematics of Kyiv National University (1997), he enrolled in the graduate studies at the Department of integral and differential equations. In 2000, under the supervision of M.O.Perestyuk, he defended a PhD dissertation "Existence and approximations of global attractors of nonlinear evolution equations", and in 2008, under the supervision of V.S. Melnik, - the Dr.Sci. thesis "Global attractors of nonautonomous multivalued dynamical systems" . His research interests concern with theory of global attractors of infinite dimensional dynamical systems, optimal control theory, nonlinear and multivalued analysis.

O.S.Chernikova, a student of M.O.Perestyuk, has been working at the Department since 2004. In 1984, O.S.Chernikova defended the PhD thesis "Stability in systems that undergo impulsive perturbations" successfully and received a Ph.D. degree in Physics and Mathematics, in 1994 she received the rank of docent. The areas of her scientific interest are differential equations with impulsive action, stability theory.

Y.V. Loveykin, a student of I.O.Parasyuk, has been working at the Department since 2006.He conducts his research in the field of perturbation theory of integrable Hamiltonian and locally Hamiltonian systems. He is an author of more than 15 scientific papers. In 2009, Yu.V.Loveykin defended his PhD thesis "Investigation of multi-frequency oscillations of locally Hamiltonian systems that are close to integrable."

A.V. Sukretna (PhD) has been working at the Department since 2007. Hers research area is optimal control of systems with distributed parameters. Being an undergraduate student of the Department, A.V.Sukretna won the NAS of Ukraine prize for university students in 2003. In 2008, under the supervision of M.O.Perestyuk, she defended her PhD thesis "Approximate average synthesis of distributed systems."

Assistant N.V. Zadoyanchuk has been working at the Department since 2008. In 2009, N.V.Zadoyanchuk defended her PhD thesis "Differential-operator equations and inclusion of the second order with the mappings of w?o-pseudomonotone type."

O.V.Ivashchuk has been working at the Department since 2011. His research interests concern with qualitative theory of impulsive systems.

Head of department of mathematical modeling of the Bogolyubov Institute of Theoretical Physics of National Academy of Sciences of Ukraine M.S.Gonchar works as professor on hourly basis at the Department.

M.S.Gonchar was born on December 27, 1944 in Bukovina, he graduated from Physics and Mathematics Faculty at the University of Chernivtsi (1969), and in 1973 he received a degree of Candidate of Sciences, in 1985 - Doctor of Science and a rank of professor (1998). His research interests are focused on mathematical problems of statistical mechanics of condensed state, problems of quantum field theory, the theory of economic equilibrium and dynamics, modelling of the stock market processes.

P.O.Kasyanov, a student of V.S. Melnik, conducts research on nonlinear analysis of physical processes and fields. P.O.Kasyanov is the winner of international and national student math competitions, the winner of the NAS of Ukraine prize for university students in 2004 and Prize of NAS of Ukraine for young scientists in 2008 (with G.M. Shevchenko). In 2007 P.O.Kasyanov defended his PhD thesis "Differential-operator inclusions in Banach spaces with w? -pseudomonotone mappings", and in 2010 - his Dr.Sci. thesis "Differential-operator inclusions and multivariational inequalities in infinite-dimensional spaces with the mappings of pseudomonotone type" .

Galary

Taras Shevchenko National University of Kyiv
Integral and Differential Equations Department
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