Limited and periodical solutions of one differential equation and its stochastic analog in the Banach space
Theorems are proved on the existence and uniqueness of bounded and periodic solutions of a linear difference equation with operator coefficients in Banach space. For the stochastic analogue of the investigated equation, the existence and uniqueness are proved of solutions of a special form, periodic...
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| Date: | 1991 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1991
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9303 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865795215346892800 |
|---|---|
| author | Gorodny , M. F. Городний , М. Ф. |
| author_facet | Gorodny , M. F. Городний , М. Ф. |
| author_institution_txt_mv | [
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"author": "М. Ф. Городний ",
"institution": "Киев. ун-т"
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| author_sort | Gorodny , M. F. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-06-19T08:20:09Z |
| description | Theorems are proved on the existence and uniqueness of bounded and periodic solutions of a linear difference equation with operator coefficients in Banach space. For the stochastic analogue of the investigated equation, the existence and uniqueness are proved of solutions of a special form, periodic and stationary in the narrow sense. |
| first_indexed | 2026-03-24T03:45:26Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9303 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:45:26Z |
| publishDate | 1991 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-93032025-06-19T08:20:09Z Limited and periodical solutions of one differential equation and its stochastic analog in the Banach space Ограниченные и периодические решения одного разностного уравнения и его стохастического аналога в банаховом пространстве Gorodny , M. F. Городний , М. Ф. Theorems are proved on the existence and uniqueness of bounded and periodic solutions of a linear difference equation with operator coefficients in Banach space. For the stochastic analogue of the investigated equation, the existence and uniqueness are proved of solutions of a special form, periodic and stationary in the narrow sense. Доказаны теоремы о существовании и единственности ограниченных и периодических решений одного линейного разностного уравнения с операторными коэффициентами в банаховом пространстве. Для стохастического аналога исследуемого уравнения доказано существование и единственность стационарных в узком смысле и периодических решений специального вида. Доведено теореми про існування і єдиність обмежених і періодичних розв’язків одного лінійного різницевого рівняння з операторними коефіцієнтами в банаховому просторі. Для стохастичного аналогу досліджуваного рівняння доведено існування і єдиність стаціонарних у вузькому розумінні і періодичних розв’язків спеціального виду. Institute of Mathematics, NAS of Ukraine 1991-01-18 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/9303 Ukrains’kyi Matematychnyi Zhurnal; Vol. 43 No. 1 (1991); 41-46 Український математичний журнал; Том 43 № 1 (1991); 41-46 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/9303/10478 Copyright (c) 1991 М. Ф. Городний |
| spellingShingle | Gorodny , M. F. Городний , М. Ф. Limited and periodical solutions of one differential equation and its stochastic analog in the Banach space |
| title | Limited and periodical solutions of one differential equation and its stochastic analog in the Banach space |
| title_alt | Ограниченные и периодические решения одного разностного уравнения и его стохастического аналога в банаховом пространстве |
| title_full | Limited and periodical solutions of one differential equation and its stochastic analog in the Banach space |
| title_fullStr | Limited and periodical solutions of one differential equation and its stochastic analog in the Banach space |
| title_full_unstemmed | Limited and periodical solutions of one differential equation and its stochastic analog in the Banach space |
| title_short | Limited and periodical solutions of one differential equation and its stochastic analog in the Banach space |
| title_sort | limited and periodical solutions of one differential equation and its stochastic analog in the banach space |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9303 |
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