On the solvability of a complete second-order differential equation in Banach space
For the complete second-order differential equation with unbounded operator coefficients $u'' + A(t)u' + B(i)u = f, \quad u(0) = u_o, \quad u'(0)=u_1$ the Cauchy problem is studied. By using the "coinmutant method", we construct the coercive sol...
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| Date: | 1993 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5950 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512173960200192 |
|---|---|
| author | Gershtein, L. M. Герштейн, Л. М. Герштейн, Л. М. |
| author_facet | Gershtein, L. M. Герштейн, Л. М. Герштейн, Л. М. |
| author_sort | Gershtein, L. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:21:43Z |
| description | For the complete second-order differential equation with unbounded operator coefficients $u'' + A(t)u' + B(i)u = f, \quad u(0) = u_o, \quad u'(0)=u_1$ the Cauchy problem is studied.
By using the "coinmutant method", we construct the coercive solution of this problem is in the Holder space in the case where the operator $В$ has the same "strength" as the operator $А^2$. |
| first_indexed | 2026-03-24T03:24:35Z |
| format | Article |
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| id | umjimathkievua-article-5950 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:24:35Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/9e/79b7837f2f4910d4b74b30e3c17e619e.pdf |
| spelling | umjimathkievua-article-59502020-03-19T09:21:43Z On the solvability of a complete second-order differential equation in Banach space О разрешимости полного дифференциального уравнения второго порядка в банаховом пространстве Gershtein, L. M. Герштейн, Л. М. Герштейн, Л. М. For the complete second-order differential equation with unbounded operator coefficients $u'' + A(t)u' + B(i)u = f, \quad u(0) = u_o, \quad u'(0)=u_1$ the Cauchy problem is studied. By using the "coinmutant method", we construct the coercive solution of this problem is in the Holder space in the case where the operator $В$ has the same "strength" as the operator $А^2$. Розглядається задача Коші для повного диференціального рівняння другого порядку з необмеженими операторними коефіцієнтами $u'' + A(t)u' + B(i)u = f, \quad u(0) = u_o, \quad u'(0)=u_1$. За допомогою "методу комутанта" встановлюється коерцитивний розв’язок задачі в просторі Гельдера у випадку, коли оператор $В$ має „силу” оператора $А^2$. Institute of Mathematics, NAS of Ukraine 1993-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5950 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 10 (1993); 1449–1454 Український математичний журнал; Том 45 № 10 (1993); 1449–1454 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5950/8583 https://umj.imath.kiev.ua/index.php/umj/article/view/5950/8584 Copyright (c) 1993 Gershtein L. M. |
| spellingShingle | Gershtein, L. M. Герштейн, Л. М. Герштейн, Л. М. On the solvability of a complete second-order differential equation in Banach space |
| title | On the solvability of a complete second-order differential equation in Banach space |
| title_alt | О разрешимости полного дифференциального уравнения второго порядка в банаховом пространстве |
| title_full | On the solvability of a complete second-order differential equation in Banach space |
| title_fullStr | On the solvability of a complete second-order differential equation in Banach space |
| title_full_unstemmed | On the solvability of a complete second-order differential equation in Banach space |
| title_short | On the solvability of a complete second-order differential equation in Banach space |
| title_sort | on the solvability of a complete second-order differential equation in banach space |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5950 |
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