On sufficient conditions for the existence of bounded solutions of inhomogeneous linear extensions of dynamical systems
We study sufficient conditions for the existence of bounded solutions of linear extensions of the dynamical systems.
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| Date: | 2010 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2010
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2891 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860508882782126080 |
|---|---|
| author | Grechko, A. L. Гречко, А. Л. |
| author_facet | Grechko, A. L. Гречко, А. Л. |
| author_sort | Grechko, A. L. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T19:39:51Z |
| description | We study sufficient conditions for the existence of bounded solutions of linear extensions of the dynamical systems. |
| first_indexed | 2026-03-24T02:32:16Z |
| format | Article |
| fulltext |
UDK 517.928
A. L. Hreçko (Nac. texn. un-t Ukra]ny „KPI”, Ky]v)
PRO DOSTATNI OZNAKY ISNUVANNQ
OBMEÛENYX ROZV’QZKIV NEODNORIDNYX
LINIJNYX ROZÍYREN| DYNAMIÇNYX SYSTEM
Sufficient conditions for the existence of bounded solutions of linear extensions of dynamical systems
are studied.
Yzuçagtsq dostatoçn¥e uslovyq suwestvovanyq ohranyçenn¥x reßenyj lynejn¥x rasßyrenyj
dynamyçeskyx system.
Pytannq isnuvannq netryvial\nyx obmeΩenyx rozv’qzkiv linijnyx neodnoridnyx
system dyferencial\nyx rivnqn\ vyvçalos\ u bahat\ox robotax (dyv., napryklad,
[1 – 3]). Na poçatku 60-x rokiv 20 stolittq v teori] obmeΩenyx rozv’qzkiv
linijnyx neodnoridnyx dyferencial\nyx system z’qvylos\ odne z holovnyx po-
nqt\ qkisno] teori] dyferencial\nyx rivnqn\ ta dynamiçnyx system — eksponen-
cial\na dyxotomiq, qka bezposeredn\o pov’qzana z isnuvannqm [dynoho obmeΩe-
noho na vsij osi rozv’qzku linijnoho dyferencial\noho rivnqnnq. Vodnoças
©runtovni doslidΩennq A. M. Samojlenka wodo zbereΩennq invariantnyx mno-
hovydiv pry zburennqx vyqvylysq tisno pov’qzanymy z pytannqmy isnuvannq ob-
meΩenyx rozv’qzkiv linijnyx rozßyren\ dynamiçnyx system [2 – 4]. V ostanni ro-
ky bahato z cyx rezul\tativ poßyreno na neskinçennovymirnyj vypadok [5 – 7].
1. Postanovka zadaçi ta oznaçennq. Rozhlqnemo linijne neodnoridne roz-
ßyrennq ta vidpovidne linijne odnoridne rozßyrennq dynamiçno] systemy
ϕt b( ) :
ϕt b B B( ) : × →R ,
dx
dt
A b x f bt t= +( ( )) ( ( ))ϕ ϕ , (1)
ϕt b B B( ) : × →R ,
dx
dt
A b xt= ( ( ))ϕ , (2)
de B — zv’qznyj kompaktnyj metryçnyj prostir, x n∈R , b B∈ , A b
|
| id | umjimathkievua-article-2891 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:32:16Z |
| publishDate | 2010 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/29/303d1c4b3ddd035ae2f067d746a70729.pdf |
| spelling | umjimathkievua-article-28912020-03-18T19:39:51Z On sufficient conditions for the existence of bounded solutions of inhomogeneous linear extensions of dynamical systems Про достатні ознаки існування обмежених розв'язків неоднорідних лінійних розширень динамічних систем Grechko, A. L. Гречко, А. Л. We study sufficient conditions for the existence of bounded solutions of linear extensions of the dynamical systems. Изучаются достаточные условия существования ограниченных решений линейных расширений динамических систем. Institute of Mathematics, NAS of Ukraine 2010-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/2891 Ukrains’kyi Matematychnyi Zhurnal; Vol. 62 No. 5 (2010); 604–611 Український математичний журнал; Том 62 № 5 (2010); 604–611 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/2891/2533 https://umj.imath.kiev.ua/index.php/umj/article/view/2891/2534 Copyright (c) 2010 Grechko A. L. |
| spellingShingle | Grechko, A. L. Гречко, А. Л. On sufficient conditions for the existence of bounded solutions of inhomogeneous linear extensions of dynamical systems |
| title | On sufficient conditions for the existence of bounded solutions of inhomogeneous linear extensions of dynamical systems |
| title_alt | Про достатні ознаки існування обмежених розв'язків неоднорідних лінійних розширень динамічних систем |
| title_full | On sufficient conditions for the existence of bounded solutions of inhomogeneous linear extensions of dynamical systems |
| title_fullStr | On sufficient conditions for the existence of bounded solutions of inhomogeneous linear extensions of dynamical systems |
| title_full_unstemmed | On sufficient conditions for the existence of bounded solutions of inhomogeneous linear extensions of dynamical systems |
| title_short | On sufficient conditions for the existence of bounded solutions of inhomogeneous linear extensions of dynamical systems |
| title_sort | on sufficient conditions for the existence of bounded solutions of inhomogeneous linear extensions of dynamical systems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/2891 |
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