Mykola Perestyuk





POSITION 
 Head of the Department of Integral and Differential Equations

Taras Shevchenko National University of Kyiv, Academician of the Academy of Sciences of Ukraine, Professor

WORK EXPERIENCE
 1969–1976

Assistant Professor of the Department of Integral and Differential Equations Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

1976–1987

Associate Professor of the Department of Integral and Differential Equations Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

1987–1988

Professor of the Department of Integral and Differential Equations Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

1988 - Present 

Head of the Department of Integral and Differential Equations Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

1987-2003

Dean of the Faculty of Mechanics and Mathematics Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

EDUCATION AND TRAINING
 1963-1968 

Student

Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

1968-1971

Graduate student,  Master Degree in Mathematics Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)

1972 

PhD Taras Shevchenko National University of Kiev, Kyiv (Ukraine)

1986 

Doctor of Sciences (Mechanics and Mathematics), DSc Taras Shevchenko National University of Kiev, Kyiv (Ukraine)

1997

Corresponding Member of the National Academy of Sciences of Ukraine

2009 

Academician of National Academy of Sciences of Ukraine 

Theories of impulse systems and the theory of invariant sets of differential and difference equations. Existence of periodic solutions of nonlinear systems with impulse action

Research Fields:
Mathematics

Previous and Current Research

Investigation of qualitative behavior of impulse systems of differential equations.

The main directions of scientific activity:

            The development of the theory and methods of solution to problems of differential and difference equations

             M.O. Perestyuk was the first to establish effective criteria for the stability of solutions of differential equations with impulse action both at fixed moments of time and at the moments of the imaging point falling into a given set of extended phase space.

            Algorithms for the approximate solution of a sufficiently wide class of differential equations with impulse action have also been developed, analogues of M.M.Bogolyubov’s theorems on substantiation of the averaging method have been proved, signs of the existence of solutions corresponding to discontinuous oscillatory modes have been established.

            M.O. Perestyuk is a laureate of the State Prize of Ukraine in the field of science and technology for the series of works "New mathematical methods in nonlinear analysis"(1996), he is a laureate of the M.M.Krylov Prize of the National Academy of Sciences of Ukraine for the series of works "Modern methods of studying dynamic systems" (1998). In 2002, by a decree of the President of Ukraine, he was awarded the honorary title of "Honored Worker of Science and Technology of Ukraine". In 2012, Perestyuk as a member of the author's team received the State Prize of Ukraine in the field of education for the educational and methodological set "Differential Equations". Perestyuk MO twice awarded the Order of Merit (2009 and 2019) for outstanding services in the creation and development of world-famous domestic scientific schools.

Currently, Perestyuk M.O. is the head of the Comprehensive Scientific Program "Modern Mathematical Problems of Science, Economics and Finance".

            M.O. Perestyuk is the chairman of the expert Council of the Ministry of Education and Science in the specialty "Mathematics, Mechanics", he is also a member of the specialized scientific council for the defense of PhD and doctoral dissertations D 26.001.37 at the Taras Shevchenko National University of Kyiv.

Perestyuk M.O. is the scientific supervisor of the interdepartmental research thema "Development of new analytical-geometric, asymptotic and qualitative methods for the study of invariant sets of differential equations". Nine scientists-mathematicians are involved in the implementation of this topic, including five doctors of sciences (DSc).

 Cooperation with the editorial boards of the following foreign journals:

“Memoirs Differential Equations and Mathematical Physics” I. Javakhishvili Tbilisi state university A.Razmadze mathematical institute, Georgia;

“Miskolc Matematical Notes” Miskolc university press, Hungary;

“Asian-European Journal of Mathematics”, World Scientific. New Jersey, London, Singapore, Beijing, Shanghai, Hong Kong, Taipei, Chennai, Tokyo.



Future Projects and Goals

One of the promising areas of scientific activity is the development of a general theory of stability of evolutionary systems with impulse impact.

Selected Publications

1. Samoilenko A.M.,  Perestyuk M.O. Impulsive differential equations. World Scientific Singapure* New Jersey*London*Hong Kong, 1995, 462.

2. Perestyuk M.O., V.A.Plotnikov, Samoilenko A.M., N.V.Skripnik. Differential equations with impulse effects: multivalued right- hand sides with discontinuities. 2011 Walter de Gruyter GmbH &Co. RG, Berlin\Boston. 307 p.

3. Samoilenko A.M., Perestyuk M.O., Krivoşeya S.A. Diferansiyel denklemler ve cözümlü  problemler// Sakarya, 2013, 358.

4. Perestyuk M.O., Samoilenko À.Ì., Parasyuk ².Î. Differential equations: Textbook, Almaty, 2012, 464 pp.

Contacts

pmo@univ.kiev.ua