Uniqueness of solutions of boundary-value problems for operator-differential equations on a finite segment and on a semiaxis
For the equation $L_0x(t)+L_1x′(t) + ... + L_nx^{(n)}(t) = O$, where $L_k, k = 0,1,...,n$, are operators acting in a Banach space, we establish criteria for an arbitrary solution $x(t)$ to be zero provided that the following conditions are satisfied: $x^{(1−1)} (a) = 0, 1 = 1, ..., p$, and $x^{(1−1)...
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| Date: | 1994 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1994
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5761 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511986880610304 |
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| author | Radzievskii, G. V. Радзиевский, Г. В. Радзиевский, Г. В. |
| author_facet | Radzievskii, G. V. Радзиевский, Г. В. Радзиевский, Г. В. |
| author_sort | Radzievskii, G. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:17:07Z |
| description | For the equation $L_0x(t)+L_1x′(t) + ... + L_nx^{(n)}(t) = O$, where $L_k, k = 0,1,...,n$, are operators acting in a Banach space, we establish criteria for an arbitrary solution $x(t)$ to be zero provided that the following conditions are satisfied: $x^{(1−1)} (a) = 0, 1 = 1, ..., p$, and $x^{(1−1)} (b) = 0, 1 = 1,...,q$, for $-∞ < a < b < ∞$ (the case of a finite segment) or $x^{(1−1)} (a) = 0, 1 = 1,...,p,$ under the assumption that a solution $x(t)$ is summable on the semiaxis $t ≥ a$ with its first $n$ derivatives. |
| first_indexed | 2026-03-24T03:21:37Z |
| format | Article |
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| id | umjimathkievua-article-5761 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:21:37Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/f8/7ae368533e1da7f7e5b994e0a23fddf8.pdf |
| spelling | umjimathkievua-article-57612020-03-19T09:17:07Z Uniqueness of solutions of boundary-value problems for operator-differential equations on a finite segment and on a semiaxis О единственности решений краевых задач на конечном отрезке и полуоси для операторно-дифференциальных уравнений Radzievskii, G. V. Радзиевский, Г. В. Радзиевский, Г. В. For the equation $L_0x(t)+L_1x′(t) + ... + L_nx^{(n)}(t) = O$, where $L_k, k = 0,1,...,n$, are operators acting in a Banach space, we establish criteria for an arbitrary solution $x(t)$ to be zero provided that the following conditions are satisfied: $x^{(1−1)} (a) = 0, 1 = 1, ..., p$, and $x^{(1−1)} (b) = 0, 1 = 1,...,q$, for $-∞ < a < b < ∞$ (the case of a finite segment) or $x^{(1−1)} (a) = 0, 1 = 1,...,p,$ under the assumption that a solution $x(t)$ is summable on the semiaxis $t ≥ a$ with its first $n$ derivatives. Для рівняння $L_0x(t)+L_1x′(t) + ... + L_nx^{(n)}(t) = O$, де $L_k, k = 0,1,...,n$- оператори, що діють у банаховнх просторах, встановлені ознаки рівності нулю довільного розв'язку $x(t)$, який задовольняє умову $x^{(1−1)} (a) = 0, 1 = 1, ..., p$, і $x^{(1−1)} (b) = 0, 1 = 1,...,q$, для $-∞ < a < b < ∞$ (випадок скінченного відрізка) і умову $x^{(1−1)} (a) = 0, 1 = 1,...,p,$ у припущенні сумовності розв'язку $x(t)$ та перших його $n$ похідних на півосі $t ≥ a$. Institute of Mathematics, NAS of Ukraine 1994-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5761 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 3 (1994); 279–292 Український математичний журнал; Том 46 № 3 (1994); 279–292 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5761/8206 https://umj.imath.kiev.ua/index.php/umj/article/view/5761/8207 Copyright (c) 1994 Radzievskii G. V. |
| spellingShingle | Radzievskii, G. V. Радзиевский, Г. В. Радзиевский, Г. В. Uniqueness of solutions of boundary-value problems for operator-differential equations on a finite segment and on a semiaxis |
| title | Uniqueness of solutions of boundary-value problems for operator-differential equations on a finite segment and on a semiaxis |
| title_alt | О единственности решений краевых задач на конечном отрезке и полуоси для операторно-дифференциальных уравнений |
| title_full | Uniqueness of solutions of boundary-value problems for operator-differential equations on a finite segment and on a semiaxis |
| title_fullStr | Uniqueness of solutions of boundary-value problems for operator-differential equations on a finite segment and on a semiaxis |
| title_full_unstemmed | Uniqueness of solutions of boundary-value problems for operator-differential equations on a finite segment and on a semiaxis |
| title_short | Uniqueness of solutions of boundary-value problems for operator-differential equations on a finite segment and on a semiaxis |
| title_sort | uniqueness of solutions of boundary-value problems for operator-differential equations on a finite segment and on a semiaxis |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5761 |
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