Personals
Parasyuk Igor Ostapovych
Sc.D. (in Mathematics), professor
Contacts
mechanics and mathematics faculty, room 503,
phone no.: (044) 431-04-63,
e-mail: parasyuk@knu.ua
General information
Graduated from Kyiv State University in 1975 (Faculty of Mechanics and Mathematics, Diploma with Honor); Ph.D. in Mathematics (1979, Kyiv State University, Speciality: Differential equations and Mathematical Physics); Doctor of Sciences in Mathematics (1995, Institute of Mathematics NAS of Ukraine, Speciality: Differential equations). 1978–1986: assistant of professor, Department of integral and differential equations; 1986–1991, 1994-1996 : associated professor, Department of integral and differential equations, 1996 –2016: professor, Department of integral and differential equations; 2003–2007 – dean of the mechanics and mathematics faculty; 2016-2022: Head of Department of geometry, topology and dynamical systems; since 2022 – professor, Department of integral and differential equations.
Teaching activity
Main courses: «Differential equations», «Geometry of dynamical systems», «Qualitative and analytical methods of studying differential equations», «Dynamical systems», «Studies in mathematics».
Scientific work
The field of scientific interests: theory of multifrequency nonlinear oscillations and invariant manifolds, analysis of nonlinear systems on manifolds, dynamic bifurcations, nonlinear singular boundary value problems on infinite intervals for ordinary differential equations.
Main publications
1. Parasyuk I.O., Protsak L.V. Existence and asymptotic properties of the solution of a nonlinear boundary-value problem on the real axis // Journal of Mathematical Sciences. 2022. Vol. 263, no. 2. P. 248-257.
2. Luchko A., Parasyuk I. Asymptotic phase for flows with exponentially stable partially hyperbolic invariant manifolds// Electronic Journal of Qualitative Theory of Differential Equations. 2021. No. 36. P. 1–28.
3. Parasyuk I. Landau–Kolmogorov type inequalities for curves on Riemannian manifolds // Mathematical Inequalities and Applications. 2019.Vol. 22, no. 2. P. 433–443.
4. Parasyuk, I. O. Quasiperiodic Forced Oscillations of a Solid Body in the Field of a Quadratic Potential // Journal of Mathematical Sciences. 2019. Vol. 240, no. 3. P. 323–341.
5. Parasyuk I. O. Hyperbolic quasiperiodic solutions of U-monotone systems on Riemannian manifolds // Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis. 2019. Vol. 26, no. 1. P. 21–52.
6. Parasyuk I., Repeta B. Dynamical bifurcation in a system of coupled oscillators with slowly varying parameters// Electronic Journal of Differential Equations. 2016.Vol. 2016, no. 233.P. 1–32.
7. Parasyuk I. Quasiperiodic Extremals of Nonautonomous Lagrangian Systems on Riemannian Manifolds // Ukrainian Mathematical Journal. 2015. Vol. 66, no. 10. P. 1553–1574.
8. Samoilenko A. M., Parasyuk I. O., Repeta B. V. Dynamical bifurcation of multifrequency oscillations in a fast-slow system // Ukrainian Mathematical Journal. 2015.Vol. 67, no. 7. P. 1008–1037.
9. Lahoda V., Parasyuk I. Theorem on the existence of an invariant section over Rm for the indefinite monotone system in R^n // Ukrainian Mathematical Journal.2013.Vol. 65, no. 1. P. 114–131.
10. Samoilenko A. M., Parasyuk I.O., Lahoda V.A. Lipschitz invariant tori of indefinite-monotone systems// Ukr Math J. 2012. Vol. 64. P. 408–432.
11. Parasyuk I., Rustamova A. Variational approach for weak quasiperiodic solutions of quasiperiodically excited Lagrangian systems on Riemannian// Electronic Journal of Differential Equations. 2012.Vol. 2012, no. 66. P. 1–22.
12. Vakal Yu. E., Parasyuk I. O. Estimation of the number of ultrasubharmonics for a twodimensional almost autonomous Hamiltonian system periodic in time// Ukrainian Mathematical Journal. 2012. Vol. 64, no. 4.P. 525–554.
13. Vakal Yu. E., Parasyuk I. O. Estimate for the number of perturbed ultrasubharmonics of a system with one and a half degrees of freedom close to a Hamiltonian // Nonlinear Oscillations. 2011.Vol. 14, no. 2. P. 149–186.
14. Horishna Yu., Parasyuk I., Protsak L. Integral representation of solutions to boundary-value problems on the half-line for linear ODEs with singularity of the first kind // Electronic Journal of Differential Equations. 2008. Vol. 2008.
15. Denysenko O. M., Parasyuk I. O. Construction of the boundaries of instability zones for the quasiperiodic Schr?odinger equation with trigonometric potential// Nonlinear Oscillations. 2007. Vol. 10, no. 1. P. 78–87.
16. Loveikin, Yu. V. Parasyuk I. O. Invariant tori of locally Hamiltonian systems close to conditionally integrable systems// Ukrainian Mathematical Journal. 2007.Vol. 59, no. 1. P. 70–99.
17. Loveikin Yu V., Parasyuk I. O. Bifurcation of coisotropic invariant tori under locally Hamiltonian perturbations of integrable systems and nondegenerate deformation of symplectic structure // Nonlinear Oscillations. 2006.Vol. 9, no. 2.P. 215–225.
18. Loveikin Yu. V., Parasyuk I. O. Theorem on perturbation of coisotropic invariant tori of locally Hamiltonian systems and its applications // Nonlinear Oscillations. 2005.Vol. 8, no. 4.P. 487–512.
19. Denysenko O. M., Parasyuk I. O. Construction of Floquet–Bloch Solutions and Estimation of Lengths of Resonance Zones of One-Dimensional Schr?odinger Equation with Smooth Potential // Ukrainian Mathematical Journal. 2004.Vol. 56, no. 1. P. 1–21.
20. Parasyuk I. O., Pozur S. V. Singular Nonlinear Eigenvalue Problem for a Second-Order Differential Equation with Energy Dissipation // Nonlinear Oscillations.2002.Vol. 5, no. 3. P. 338–359.
21. Kubichka A. A., Parasyuk I. O. Bifurcation of a Whitney-smooth family of coisotropic invariant tori of a Hamiltonian system under small deformations of a symplectic structure // Ukrainian Mathematical Journal. 2001.Vol. 53, no. 5.P. 701–718.
22. Zakharin S. F., Parasyuk I. O. Generalized and classical almost periodic solutions of Lagrangian systems // Funkcialaj Ekvacioj Serio Internacia. 1999. Vol. 42, no. 3. P. 325– 338.
23. Parasyuk I. O. Bifurcation of a Cantor set of coisotropic invariant tori of Hamiltonian systems under perturbation of symplectic structure // Nelin. Kolyvannya.1998.Vol. 1, no. 2.P. 81–89.
24. Samoilenko A. M., Parasyuk I. O. Nilpotent flows of S^1-invariant Hamiltonian systems on 4- dimensional symplectic manifolds // Ukrainian Mathematical Journal.1997.Vol. 49, no. 1. P. 135–155.
25. Parasyuk, I. O. Reduction and coisotropic invariant tori of Hamiltonian systems with non-poisson commutative symmetries. I, II // Ukrainian Mathematical Journal.1994.Vol. 46, no. 5. P. 572–580, no. 7.P. 991–1002.
26. Parasyuk I. O. Variables of the action-angle type on symplectic manifolds stratified by coisotropic tori // Ukrainian Mathematical Journal.1993.Vol. 45, no. 1. P. 85–93.
27. Parasyuk I. O. Coisotropic invariant tori of Hamiltonian systems of the quasiclassical theory of motion of a conduction electron // Ukrainian Mathematical Journal.1990.Vol. 42, no. 3. P. 308–312.
28. Parasyuk I. O. Conservation of multidimensional invariant tori of Hamiltonian systems // Ukrainian Mathematical Journal. 1984. Vol. 36, no. 4. P. 380–385.
29. Parasyuk I. O. Conservation of quasi-periodic movements of reversible multifrequency systems // Dopovidi Akademii Nauk Ukrainskoi RSR seriya a-fiziko-matematichni ta technichni nauki.1982. no. 9. P. 18–21.
30. Parasyuk I. O. Zones of instability of the Schr?odinger equation with a smooth quasiperiodic potential // Ukrainian Mathematical Journal.1978.Vol. 30, no. 1. P. 50–56.
© Taras Shevchenko National University of Kyiv
Integral and Differential Equations Department
All rights reserved