Dynamics of solutions of the simplest nonlinear boundary-value problems
We investigate two classes of essentially nonlinear boundary-value problems by using methods of the theory of dynamical systems and two special metrics. We prove that, for boundary-value problems of both these classes, all solutions tend (in the first metric) to upper semicontinuous functions and, u...
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| Date: | 1999 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
1999
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4668 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510826982539264 |
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| author | Romanenko, O. Yu. Sharkovsky, O. M. Романенко, О. Ю. Шарковський, О. М. |
| author_facet | Romanenko, O. Yu. Sharkovsky, O. M. Романенко, О. Ю. Шарковський, О. М. |
| author_sort | Romanenko, O. Yu. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:11:00Z |
| description | We investigate two classes of essentially nonlinear boundary-value problems by using methods of the theory of dynamical systems and two special metrics. We prove that, for boundary-value problems of both these classes, all solutions tend (in the first metric) to upper semicontinuous functions and, under sufficiently general conditions, the asymptotic behavior of almost every solution can be described (by using the second metric) by a certain stochastic process. |
| first_indexed | 2026-03-24T03:03:11Z |
| format | Article |
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| id | umjimathkievua-article-4668 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:03:11Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/f9/e0c44d8284a74d9ea672699087b80cf9.pdf |
| spelling | umjimathkievua-article-46682020-03-18T21:11:00Z Dynamics of solutions of the simplest nonlinear boundary-value problems Динаміка розв'язків найпростіших нелінійних граничних задач Romanenko, O. Yu. Sharkovsky, O. M. Романенко, О. Ю. Шарковський, О. М. We investigate two classes of essentially nonlinear boundary-value problems by using methods of the theory of dynamical systems and two special metrics. We prove that, for boundary-value problems of both these classes, all solutions tend (in the first metric) to upper semicontinuous functions and, under sufficiently general conditions, the asymptotic behavior of almost every solution can be described (by using the second metric) by a certain stochastic process. Методами теорії динамічних систем досліджуються два класи істотно нелінійних граничних задач. При цьому використовуються дві спеціальні метрики. Показано, що для граничних задач з обох цих класів всі розв'язки прямують (у першій метриці) до иапівиеперервних зверху функцій, а при досить загальних умовах" асимптотична поведінка майже кожного розв'язку описується (за допомогою другої метрики) деяким стохастичиим процесом. Institute of Mathematics, NAS of Ukraine 1999-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4668 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 6 (1999); 810–826 Український математичний журнал; Том 51 № 6 (1999); 810–826 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4668/6038 https://umj.imath.kiev.ua/index.php/umj/article/view/4668/6039 Copyright (c) 1999 Romanenko O. Yu.; Sharkovsky O. M. |
| spellingShingle | Romanenko, O. Yu. Sharkovsky, O. M. Романенко, О. Ю. Шарковський, О. М. Dynamics of solutions of the simplest nonlinear boundary-value problems |
| title | Dynamics of solutions of the simplest nonlinear boundary-value problems |
| title_alt | Динаміка розв'язків найпростіших нелінійних
граничних задач |
| title_full | Dynamics of solutions of the simplest nonlinear boundary-value problems |
| title_fullStr | Dynamics of solutions of the simplest nonlinear boundary-value problems |
| title_full_unstemmed | Dynamics of solutions of the simplest nonlinear boundary-value problems |
| title_short | Dynamics of solutions of the simplest nonlinear boundary-value problems |
| title_sort | dynamics of solutions of the simplest nonlinear boundary-value problems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4668 |
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