Pokutnyi Oleksander Oleksiyovich
Publications
AMS MathSciNet.
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2023
1. Pokutnyi O.O. Roughness of dichotomy for the connected system of operator-differential equations in Banach spaces, arxiv.org: 2304.12859, 2023.
2. Pokutnyi O.O. Weakly nonlinear hyperbolic differential equation in Hilbert space, arxiv.org: 2304.09746, 2023.
2022
1. Impulse boundary-value problem for the Lyapunov equation with values in the Hilbert space, Nonlinear oscillations, with Panasenko E.V., 2022, v.25, No.4, p. 361-369.
2021
1. Autonomous nonlinear boundary value problems for the Lyapunov equation in the Hilbert space, with Bihun D.S, Panasenko E.V., Ukrainian mathematical journal, 2021, v.73, No. 7, p. 867 – 878.
2. Minimizing of the quadratic functional on Hopfield networks, with Boichuk A.A., Feruk V.A. and Bihun D.S, Electronic journal of qualitative theory of differential equations, 2021, No. 92, https://doi.org/10.14232/ejqtde.2021.1.92
2020
1. Bounded solutions of evolution equations. I, with D. S. Bihun, I. G. Kliuchnyk, M. I. Sadoviy, O. M. Tryfonova, Nonlinear oscillations (Journal of mathematical sciences), 2020, 23, No.3, p. 291-320.
2. Bounded solutions of evolution equations, preprint, 2020.
2019
1. Bifurcation of solutions of the second order boundary value problems in Hilbert spaces, with Boichuk A.A., Miskolc Mathematical Notes, 2019, No. 1, p.139-152.
2. Bounded solutions of nonlinear Lyapunov equation and homoclinic chaos, with Boichuk O.A., Ukrainian mathematical journal, 2019, 71, v.6, p. 761-773.
3. Boundary value problems for the evolution Schrodinger equation. Part I, Nonlinear oscillations (Journal of mathematical sciences), 2019, 22, v.2, p.235-249.
4. Boundary-value problems for the evolutionary Schrodinger equation. Part II, Nonlinear oscillations (Journal of mathematical sciences), with Bihun D.S., 2019, 22, No.4, p. 439-457.
5. Bifurcation conditions for the solutions of the Lyapunov equation in a Hilbert space, with Panasenko E.V., Journal of Mathematical Sciences, 2019, 236:3, 313-332,
https://link.springer.com/article/10.1007/s10958-018-4113-5
6. Boundary value problems for the evolution Schrodinger equation, preprint, 2019.
7. Homoclinic chaos and Navier-Stokes equations. Mathematical and computer modeling, 2019, 19, p.112-118.
8. Probability of traumatic situations in mechanized processes in agriculture using mathematical apparatus of markov chain method, with Voinalovych O., Hnatiuk O., Rogovskii I, 18th international scientific conference engineering for rural development, p.563-569, doi: 10.22616/ERDev2019.18.N245, Proceedings paper
2018
1. Bounded solutions of evolution equations, Ukrainian mathematical journal, 2018, v.70, No.1, p. 7 -29.
2. Nonlinear boundary value problems for the Lyapunov equation in the space Lp. Nonlinear oscillations, with Panasenko E.V., 2018, v. 21, ¹4. - p. 523 — 536.
3. Exponential dichotomy and bifurcation conditions of solutions of the Hamiltonian operators boundary value problems in the Hilbert space. Mathematics and Statistics, vol. 6(1), 2018. - p. 9-15.
2017
1. Theory of boundary value problems of operator-differential equations. (According to the materials of scientific report at the meeting of the Presidium of National Academy of Sciences of Ukraine November 9, 2016), Bulletin of the National Academy of Sciences of Ukraine, 2017, 1. - p. 89-97.
2. Bifurcation theory of the Schredinger equation, with Boichuk O.A., Differential equations, 2017, vol.53, No.7, p.882-890.
3. Boundary value problems for the Schredinger equation with conditions at infinity, Proceedings of the 4th Conference of Mathematical Society of Moldova, CMSM4’2017, June 28 – July 2, 2017, Chisinau, Republic of Moldova, p. 321-324.
2016
1. Boundary value problems for Lyapunov equation in the Banach space, with Panasenko E.V. Nonlinear oscillations (Nelinijni kolivannya), 2016, v.19, No.2. – p. 240 – 246.
2. Development of the methods of solvability of boundary value problems for operator- differential equations which simulate physical, technical and biological problems, with Bondar I. National Academy of Sciences, Institute of mathematics, preprint, 2016, 35 p.
3. Using of the methodology of investigation of Markov random processes for forecasting of behavior , with Bilko T.O., Gnatyuk O.A. Naukoviy Vestnik Nacional’nogo universitetu boiresursiv ta prirodokoristuvannya Ukraini, 2016, 241. – p. 85 – 95.
2015
1. "Boundary Value Problem for an
Operator-Differential Riccati Equation in the
Hilbert Space on the Interval", Advances in Pure Mathematics, 2015, 5, 865-873
Published Online December 2015 in SciRes. "http://www.scirp.org/journal/apm
http://dx.doi.org/10.4236/apm.2015.514081">
2014
1. "Solutions of the Schrödinger equation in a Hilbert space", with Boichuk A. A, Boundary Value Problems. — 2014.
2013
1. "Dichotomy and boundary value problems on the whole line", with Boichuk A. A., Chaotic modeling and simulation (CMSIM). — 2013. — No. 2. — p. 247–255.
2. "Exponential dichotomy and bounded solutions of the Schrodinger equation", Proceedings, 6th Chaotic Modeling and Simulation International Conference, 11–14 June 2013 Istanbul, Turkey. — p.97–103.
3. "Periodic solution of Hill’s equation", Nonlinear oscillations (Neliniini kolyvannia). — 2013. — v. 16, No. 1. — p. 111–117.
4. "Development of the Neimann’s series method of generalized invertibility on the spectrum of an operator in Banach and Frechet spaces", Reports of the National Academy of Sciences of Ukraine. — 2013. — No. 1. — p. 19–23.
5. "Normally-resolvable operator equations" (in Russian), with Boichuk A. A., Zhuravlyov V. F., Ukrainian Mathematical Journal. — 2013. — v. 65, No. 2. — p. 163–175.
6. "Application of ergodic theory to the study of the boundary value problem with periodic operator coefficient" (in Russian), with Boichuk A.A., Ukrainian Mathematical Journal. — 2013. — V. 65, No. 3. — p. 329–339.
7. "Application of perturbation theory to the solvability analysis of differential algebraic equations", with A. A. Boichuk, V. F. Chistyakov, Computational Mathematics and Mathematical Physics. — 2013. — v. 53, No. 6. — p. 777–788.
8. "Analysis of Solvability for Weak Nonlinear Differential Algebraic Systems" (in Russian), with Perepelitsa M. A., Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software". — 2013. — vol. 6, no. 4. — p. 55–62.
9. "Controllability of evolution Sobolev-Galpern’s equation with pure delay" (in Russian), with Semenov V. V., Mathematical and computer modelling. — 2013. — V. 8. — p. 190–197.
10. "Boundary value problems for differential equations in Banach space with unbounded operator in the linear part" (in Ukrainian), with Panasenko E. V., Nonlinear oscillations (Neliniini kolyvannia). — 2013. — v. 16, No. 4. — p. 518–526.
2012
1. "Bifurcation of two-point boundary value problem for Hill’s equation" (in Russian), Journal of numerical and applied mathematics. — 2012. — No. 4 (110). — p. 77–85.
2. "Linear normally-resolvable equations in Banach spaces" (in Russian), Journal of numerical and applied mathematics. — 2012. — No. 1 (107). — p. 146–153.
3. "Bounded solutions of linear and weakly nonlinear differential equations in Banach space with unbounded linear part", Differential equations. — 2012. — v. 48, No. 6. — p. 803–813.
4. "Dichotomy and boundary value problems on the whole line", with Boichuk A. A., Proceedings, 5th Chaotic Modeling and Simulation International Conference, 12–15 June 2012, Athens Greece. — p. 81–89.
2011
1. "Application of Ergodic Theory for solving a family of difference equations in Banach space", with Boichuk A. A., Math. Analysis Differential Equations and Applications, Bulgaria. — 2011. — p. 101–106.
2. "Approximation of generalized bounded solutions of evolutionary equations with unbounded operator ", Nonlinear oscillations (Neliniini kolyvannya). —2011. — vol. 14, No. 1. — P. 93–99.
"3. "Periodic problems of difference equations and Ergodic Theory", with Biletskyi B. A., Boichuk A. A, Abstract and Applied Analysis.
2010
1. "New formulas for finding matrix generalized inverse" (in Russian), Journal of computational and applied mathematics. — 2010. — No. 1 (102). — p. 115–120.
2009
1. "Generalized bounded solutions of linear evolutionary equations in locally convex spaces"(in Russian), Journal of computational and applied mathematics. — 2009. — No. 2 (98). — p. 35–40.
2008
1. "Bounded solutions of weakly nonlinear perturbed differential equations in a Banach space", with Boichuk A. A., Nonlinear Oscillations (Neliniini kolyvannya). — 2008. — vol. 11, No. 2. — p. 158–167.
2007
1. "Bounded solutions of linear perturbed differential equations in a Banach space", with Boichuk A. A., Tatra Mountains Math. Publications. — 2007. — vol. 38. — p. 29–41.
2006
1. "Bounded solutions of linear differential equations in Banach space", with Boichuk A. A., Nonlinear Oscillations (Neliniini kolyvannya). — 2006. — vol. 9, No. 1. — p. 3–15.
2. "Solutions of linear difference equations in Banach space bounded on the entire integer axis" (in Russian), Âulletin of Kiev University. — 2006. — No. 1. — p. 182–188.
3. "Solutions of linear weakly perturbed difference equations in Banach space bounded on the entire integer axis" (in Russian), Âulletin of Kiev University. — 2006. — No. 3. — p. 240–245.
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2023
1. Weakly nonlinear hyperbolic differential equation in
Hilbert space (2023).
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2. Ãðóáîñòü äèõîòîìèè Ãðóáîñòü äèõîòîìèè
3. Weak chaos in nonlinear systems Chaos in discrete systems
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