Critical cases of stability of one nonautonomous essentially nonlinear equation of the nth order
We establish sufficient conditions of the Lyapunov stability of the trivial solution of a nonautonomous ordinary differential equation of the nth order in the case where its characteristic equation has a multiple zero root. The stability is determined by nonlinear terms.
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| Date: | 1997 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5054 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511247119679488 |
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| author | Vitrychenko, I. E. Вітриченко, І. Є. |
| author_facet | Vitrychenko, I. E. Вітриченко, І. Є. |
| author_sort | Vitrychenko, I. E. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:23:40Z |
| description | We establish sufficient conditions of the Lyapunov stability of the trivial solution of a nonautonomous ordinary differential equation of the nth order in the case where its characteristic equation has a multiple zero root. The stability is determined by nonlinear terms. |
| first_indexed | 2026-03-24T03:09:51Z |
| format | Article |
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| id | umjimathkievua-article-5054 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:09:51Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/d3/288cc641aac85183ac825f0836963fd3.pdf |
| spelling | umjimathkievua-article-50542020-03-18T21:23:40Z Critical cases of stability of one nonautonomous essentially nonlinear equation of the nth order Критические случаи устойчивости одного неавтономного существенно нелинейного уравнения n-го порядка Vitrychenko, I. E. Вітриченко, І. Є. We establish sufficient conditions of the Lyapunov stability of the trivial solution of a nonautonomous ordinary differential equation of the nth order in the case where its characteristic equation has a multiple zero root. The stability is determined by nonlinear terms. Одержано достатні умови стійкості за Ляпуиовим тривіального розв'язку неавтономного звичайного диференціального рівняння n-го порядку у випадку, коли його граничне характеристичне рівняння має кратний нульовий корінь. Стійкість визначається нелінійними доданками. Institute of Mathematics, NAS of Ukraine 1997-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5054 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 5 (1997); 720–724 Український математичний журнал; Том 49 № 5 (1997); 720–724 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5054/6805 https://umj.imath.kiev.ua/index.php/umj/article/view/5054/6806 Copyright (c) 1997 Vitrychenko I. E. |
| spellingShingle | Vitrychenko, I. E. Вітриченко, І. Є. Critical cases of stability of one nonautonomous essentially nonlinear equation of the nth order |
| title | Critical cases of stability of one nonautonomous essentially nonlinear equation of the nth order |
| title_alt | Критические случаи устойчивости одного неавтономного
существенно нелинейного уравнения n-го порядка |
| title_full | Critical cases of stability of one nonautonomous essentially nonlinear equation of the nth order |
| title_fullStr | Critical cases of stability of one nonautonomous essentially nonlinear equation of the nth order |
| title_full_unstemmed | Critical cases of stability of one nonautonomous essentially nonlinear equation of the nth order |
| title_short | Critical cases of stability of one nonautonomous essentially nonlinear equation of the nth order |
| title_sort | critical cases of stability of one nonautonomous essentially nonlinear equation of the nth order |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5054 |
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