# Academician M.O. Perestyuk (January 1, 1946 – January 25, 2023) – outstanding scientist and teacher

## DOI:

https://doi.org/10.17721/1812-5409.2024/1.1## Keywords:

Mykola Oleksiiovych Perestyuk, department of integral and differential equations, mechanical and mathematical faculty, Kyiv Scientific School, differential equations, impulse differential equations## Abstract

*The article is devoted to the life and scientific path of academician of the National Academy of Sciences of Ukraine, Нonored professor of Taras Shevchenko Kyiv National University, Mykola Oleksiyovych Perestyuk. In particular, the material contains a complete list of Mykola Oleksiyovych's students and the topics of their dissertations, a list of monographs, textbooks, study guides and major scientific publications, a list of major state awards and titles.*

* Pages of the article in the issue*: 5 - 16

**Language of the article**: Ukrainian

## References

Perestyuk M., Vyshenskyi V. (2021) Combinatorics: First Steps. N.Y.: Nova Science Pub Inc.

Perestyuk M.O., Kapustyan O.V., Romanyuk I.V. (2018) Attractors of infinite-dimensional impulsive dynamical systems. Deutschland, Saarbrücken: LAP LAMBERT Academic Publishing.

Samoylenko A.M., Krivoşeya S.A., Perestyuk N.A. (2013) Diferansiyel denklemler ve cozumlu problemler. Sakarya.

Perestyuk M.O., Samoilenko А.М., Parasyuk І.О. (2012) Differential equations: Textbook. Almaty.

Perestyuk N.A., Plotnikov V.A., Samoilenko A.M., Skripnik N.V. (2011) Differential equations with impulse effects. Multivalued right-hand sides with discontinuities (2nd ed.). De Gruyter Studies in Mathematics.

Perestyuk M.O., Slyusarchuk V.Yu (2023) Method of Local Linear Approximation in the Theory of Nonlinear Impulsive Systems. Ukr. Math. J., 75(1), 118–137.

Perestyuk M.O., Slyusarchuk V.Yu. (2023) Systems with perturbations of parameters. J. Math. Sci., 270(2), 335–352.

Perestyuk M.O., Slyusarchuk V.Yu. (2022) Application of the Green–Samoilenko Function and Operator to the Investigation of Non-Lipschitz Differential Equations. Ukr. Math. J., 73(3), 1937–1957.

Perestyuk N.A. Skripnik N.V. (2018) Averaging of Fuzzy Systems. Ukr. Math. J., 70(4), 477–494.

Kapustyan O.V., Perestyuk M.O., Romanyuk I.V. (2018) Stability of Global Attractors of impulsive infinite-Dimensional Systems. Ukr. Math. J., 70(1), 30-41.

Kapustyan O.V., Perestyuk M.O., Romanyuk I.V. (2017) Global attractor of weakly nonlinear parabolic system with discontinuous trajectories. Memoirs on Diff. Eq. and Math. Ph., 72, 59-70.

Kapustyan O.V., Perestyuk M.O. (2016) Global Attractors in Impulsive Infinite-Dimensional Systems. Ukr. Math. J., 68(4), 583-597.

Perestyuk M.O., Feketa P.V. (2015) On preservation of an exponentially stable invariant torus. Tatra Mt. Math. Publ., 63(1), 215–222.

Mishura Yu., Perestyuk M., Ragulina O. (2015) Ruin probability in a risk model with a variable premium intensity and risky investments. Opuscula Mathematica, 35(3), 333–352.

Perestyuk M.O., Feketa P.V. (2014) On Preservation of the Invariant torus for Multifrequency Systems. Ukr. Math. J., 65(11), 1661–1669.

Perestyuk M.O., Klevchuk I.I. (2014) Application of Asymptotic Methods to Regularly and Singularly Perturbed Differential-Difference Equations. J. Math. Sci., 197(1), 96–107.

Perestyuk M., Mishura Y., Shevchenko G. (2014) On the distribution of integral functionals of a homogeneous diffusion process. Modern Stochastics: Theor. and App., 2014(1), 109–116.

Perestyuk N.A. Skripnik N.V. (2018) Averaging of set-valued impulsive systems. Ukr. Math. J., 65(1), 140–157.

Perestyuk M.O., Kapustyan O.V. (2012) Long-time behaviour of evolution inclusion with non-damped impulsive effects. Mem. Differ. Equ. Math. Phys., 56, 89–113.

Perestyuk M.O., Feketa P.V. (2011) On Existence and stability of Invariant Sets of Discontinuous Dynamical Systems. Mathematical analysis, differential equations and their applications. ACADEMIC Publishing house, Sofia. P. 129–138.

Perestyuk M., Feketa P. (2011) Invariant sets of impulsive differential equations with particularities in ω-limit set. Abstract and Appl. Anal. 2011. 1–14.

Perestyuk M.O., Feketa P.V. (2010) Invariant manifolds of one class of systems of impulsive differential. Nonlin. Oscil., 13(2), 260–273.

Perestyuk M.O., Slyusarchuk V.Yu. (2009) Green–Samoilenko operator in the theory of invariant sets of nonlinear differential equations. Ukr. Math. J., 61(7), 1123–1136.

Perestyuk M.O., Baloha S.I. (2008) Existence of an invariant torus for one class of systems of differential equations. Nonlin. Oscil., 11(4), 548–558.

Perestyuk M.O., Kasyanov P.O., Zadoyanchuk N.V. (2008) On solvability for the second order evolution inclusions with the Volterra type operators. Miskolc Math. Notes, 9(2),119–135.

Perestyuk M.O., Kasyanov P.O., Zadoyanchuk N.V. (2008) On Faedo-Galerkin method for evolution inclusions with -pseudomonotone maps. Memoirs on Diff. Eq. and Math. Physics, 44, 105–132.

Perestyuk M.O., Chernikova O.S. (2008) Some modern aspects of the theory of impulsive differential equations. Ukr. Math. J., 60(1), 91–107.

Perestyuk M.O., Korol’ I.I. (2006) Once again on the Samoilenko numerical-analytic method of successive periodic approximations. Ukr. Math. J., 58(4), 529–550.

Perestyuk M.O., Vlasenko L.A. (2005) On the Solvability of Impulsive Differential-Algebraic Equations. Ukr. Math. J., 57(4), 551–564.

Perestyuk M., Matarazzo G., Chernikova O. (2004) Stability of sets for impulsive differential systems. Miscols Math. Notes, 5(2), 193–201.

Perestyuk N.A., Kapustyan A.V. (2003) Global Attractor of an Evolution Inclusion with Pulse Influence at Fixed Moments of Time. Ukr. Math. J., 55(8), 1283–1294.

Perestyuk M.O., Slyusarchuk V.Yu. (2003) Conditions for the Existence of Nonoscillating Solutions of Nonlinear Differential Equations with Delay and Pulse Influence in a Banach Space. Ukr. Math. J., 55(6), 956–965.

Perestyuk M.O., Slyusarchuk V.Yu. (2003) Oscilations of nonlinear differential-integral equation in Banach space with respect to its subspace. Miscols Math. Notes, 4(1), 53–64.

Perestyuk N.A., Cherevko I.M. (2002) Investigation of the integral manifolds of singularly perturbed functional differential equations. Miskolc Math. Notes. 3(1), 47–58.

Perestyuk M.O., Chernikova O.S. (2002) On Stability of Integral Sets of Impulsive Differential Systems. Ukr. Math. J., 54(2), 306–315.

Kaplun Yu., Perestyuk M., Samoylenko V. (2001) Implicit function equation with discontinuous trajectories. Miskolc Math. Notes. 2(2), 145–157.

Perestyuk M.O., Cherevko I.M. (2001) Decomposition of linear singularly perturbed functional differential equations. Nonlin. Oscil., 4(3), 345–353.

Perestyuk M.O., Chernikova O.S. (2001) On the stability of integral sets of impulsive differential systems. Miskolc Math. Notes. 2(1), 49–60.

Perestyuk N.A., Samoilenko A.M., Stanzhitskii A.N. (2001) On the Existence of Periodic Solutions for Certain Classes of Systems of Differential Equations with Random Pulse Influence. Ukr. Math. J., 53(8), 1266–1289.

Perestyuk N.A., Chernikova O.S. (2001) On the Stability of Invariant Sets of Discontinuous Dynamical Systems. Ukr. Math. J., 53(1), 91–98.

Perestyuk N.A., Ostapenko E.V. (2000) Controlled Pulse Influence in Games with Fixed Termination Time. Ukr. Math. J., 52(8), 1274–1281.

Perestyuk N.A., Dudzyanyi S.I. (1998) On the stability of a trivial invariant torus of one class of impulsive systems. Ukr. Math. J., 50(3), 387–399.

Perestyuk N.A., Dudzyanyi S.I. (1997) On the stability of an invariant torus. Ukr. Math. J., 49(9), 1365–1376.

Perestyuk N.A., Tkach A.B. (1997) Periodic solutions of a weakly nonlinear system of partial differential equations with pulse influence. Ukr. Math. J., 49(4), 665–671.

Perestyuk N.A., Chernikova O.S. (1997) Stability of solutions of pulsed systems. Ukr. Math. J., 49(1), 109–123.

Perestyuk M., Ronto A. (1996) Numerical-analytic method for the equation of nonlinear oscillator. Publ. Univ. Miscolc, Ser. D. Natur. Sci. Math. 36(2), 115–124.

Perestyuk N.A., Ronto A.N. (1995) On a method for construction of successive approximations for investigation of multipoint boundary-value problems. Ukr. Math. J., 47(9), 1415–1426.

Perestyuk N.A., Slyusarchuk V.E. (1995) Periodic solutions of nonlinear differential equations with pulse influence in a banach space. Ukr. Math. J., 47(3), 430–442.

Akhmetov M.U., Perestyuk N.A., Tleubergenova M.A. (1995) Control over linear pulse systems. Ukr. Math. J., 47(3), 360–368.

Perestyuk N.A., Chernikova O.S. (1994) On invariance of some properties of solutions under perturbation of a pulse system of differential equations. Ukr. Math. J., 46(12), 1899–1906.

Perestyuk N.A., Samoilenko A.M., Martynyuk D.I. (1994) Reducibility of nonlinear almost periodic systems of difference equations on an infinite-dimensional torus. Ukr. Math. J., 46(9), 1336–1344.

Perestyuk N.A., Asrorov F.A. (1994) Green-Samoilenko function and existence of integral sets of linear extensions of nonautonomous equations. Ukr. Math. J., 46(8), 1172–1177.

Perestyuk N.A., Samoilenko A.M., Martynyuk D.I. (1994) Reducibility of nonlinear almost periodic systems of difference equations given on a torus. Ukr. Math. J., 46(4), 425–432.

Perestyuk N.A., Kh. M. Gulov Kh.M. (1993) Integral sets of systems of difference equations. Ukr. Math. J., 45(12), 1815–1824.

Perestyuk N.A., Akhmetov M.U. (1993) On a comparison method for pulse systems in the space R^n. Ukr. Math. J., 45(6), 826–836.

Perestyuk N.A., Akhmetov M.U. (1992) Periodic and almost periodic solutions of strongly non-linear impulsive systems. J. of App. Math. and Mech., 56(6), 829–837.

Perestyuk N.A., Vyshenskaya O.V. (1992) Integral sets of a class of discontinuous dynamical systems. Ukr. Math. J., 44(5), 528–534.

Perestyuk N.A., Akhmetov M.U. (1992) Integral sets of quasilinear pulse systems. Ukr. Math. J., 44(1), 1–7.

Perestyuk N.A., Akhmetov M.U. (1991) Asymptotic representation of solutions of regularly perturbed systems of differential equations with nonclassical right-hand side. Ukr. Math. J., 43(10), 1209–1214.

Perestyuk N.A., Ashirov O.A. (1991) Method of freezing in systems with impulse action. Ukr. Math. J., 43(6), 796–801.

Perestyuk N.A., Samoilenko A.M., Trofimchuk S.I. (1991) Generalized solutions of impulse systems and the phenomenon of pulsations. Ukr. Math. J., 43(5), 610–615.

Perestyuk N.A., Akhmetov M.U. (1991) Periodic solutions of quasilinear impulse systems in the critical case. Ukr. Math. J., 43(4), 273–279.

Perestyuk N.A., Akhmetov M.U. (1989) Stability of periodic solutions of differential equations with impulse action on surfaces. Ukr. Math. J., 41(12), 1368–1372.

Perestyuk N.A., Akhmetov M.U. (1989) Differentiable dependence of the solutions of impulse systems on initial data. Ukr. Math. J., 41(8), 878–882.

Perestyuk N.A., Akhmetov M.U. (1989) Almost-periodic solutions of nonlinear impulse systems. Ukr. Math. J., 41(3), 259–263.

Ishchuk V.V., Perestyuk N.A. (1985) Asymptotic integration of weakly nonlinear systems with impulses. Ukr. Math. J., 37(3), 288–291.

Perestyuk N.A., Akhmetov M.U. (1984) Almost-periodic solutions of one class of systems with impulses. Ukr. Math. J., 36(4), 397–401.

Perestyuk N.A., Chernikova O.S. (1984) A contribution to the stability problem for solutions of systems of differential equations with impulses. Ukr. Math. J., 36(2), 171–176.

Perestyuk N.A. (1984) Invariant sets of a class of discontinuous dynamical systems. Ukr. Math. J., 36(1), 58–62.

Perestyuk N.A., Shovkoplyas V.N. (1979) Periodic solutions of nonlinear differential equations with impulsive action. Ukr. Math. J., 31(5), 408–414.

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*Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences*,

*78*(1), 5–16. https://doi.org/10.17721/1812-5409.2024/1.1

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Copyright (c) 2024 Oksana Bezushchak, Mykhailo Horodnii, Yaroslav Zhuk, Oleksiy Kapustyan, Oleg Limarchenko, Andrii Loveikin, Yuliya Mishura, Mikhail Moklyachuk, Igor Parasyuk, Anatolii Petravchuk, Oleksandr Stanzhytskyi, Anna Sukretna, Oleksii Kharytonov, Andrii Chaikovskyi, Igor Shevchuk, Rostyslav Yamnenko

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