On the Existence of a Generalized Solution of One Partial Differential System
We propose a method for the construction of generalized solutions for some nondivergent partial differential systems using set-valued analogs of the generalized statement of the problem based on subdifferential calculus. We establish new sufficient conditions for the existence of solutions of a vari...
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| Datum: | 2002 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2002
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4163 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510297743163392 |
|---|---|
| author | Solonukha, O.V. Солонуха, О. В. Солонуха, О. В. |
| author_facet | Solonukha, O.V. Солонуха, О. В. Солонуха, О. В. |
| author_sort | Solonukha, O.V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:23:25Z |
| description | We propose a method for the construction of generalized solutions for some nondivergent partial differential systems using set-valued analogs of the generalized statement of the problem based on subdifferential calculus. We establish new sufficient conditions for the existence of solutions of a variational inequality with set-valued operator under weakened coerciveness conditions. We consider examples of a weighted p-Laplacian in the Sobolev spaces \(W_p^1 \left( \Omega \right)\) , p ≥ 2. |
| first_indexed | 2026-03-24T02:54:46Z |
| format | Article |
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| id | umjimathkievua-article-4163 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:54:46Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/a0/4ff592e36526a6377b0a89243158f4a0.pdf |
| spelling | umjimathkievua-article-41632020-03-18T20:23:25Z On the Existence of a Generalized Solution of One Partial Differential System О существовании обобщенного решения одной системы в частных производных Solonukha, O.V. Солонуха, О. В. Солонуха, О. В. We propose a method for the construction of generalized solutions for some nondivergent partial differential systems using set-valued analogs of the generalized statement of the problem based on subdifferential calculus. We establish new sufficient conditions for the existence of solutions of a variational inequality with set-valued operator under weakened coerciveness conditions. We consider examples of a weighted p-Laplacian in the Sobolev spaces \(W_p^1 \left( \Omega \right)\) , p ≥ 2. Запропоновано метод побудови узагальнених розв'язків для деяких недивергентних систем із частинними похідними за допомогою множиннозначних аналогів узагальненої постановки проблеми, що використовує субдиференціальне числення. Отримано нові достатні умови існування розв'язків варіаційної нерівності із множиннозначним оператором при послаблених умовах на коерцитивність. Розглянуто приклади вагового $p$-лапласіана у соболєвських просторах $W_p^1 \left( \Omega \right)$, $p ≥ 2.$ Institute of Mathematics, NAS of Ukraine 2002-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4163 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 9 (2002); 1250-1264 Український математичний журнал; Том 54 № 9 (2002); 1250-1264 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4163/5035 https://umj.imath.kiev.ua/index.php/umj/article/view/4163/5036 Copyright (c) 2002 Solonukha O.V. |
| spellingShingle | Solonukha, O.V. Солонуха, О. В. Солонуха, О. В. On the Existence of a Generalized Solution of One Partial Differential System |
| title | On the Existence of a Generalized Solution of One Partial Differential System |
| title_alt | О существовании обобщенного решения одной системы в частных производных |
| title_full | On the Existence of a Generalized Solution of One Partial Differential System |
| title_fullStr | On the Existence of a Generalized Solution of One Partial Differential System |
| title_full_unstemmed | On the Existence of a Generalized Solution of One Partial Differential System |
| title_short | On the Existence of a Generalized Solution of One Partial Differential System |
| title_sort | on the existence of a generalized solution of one partial differential system |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4163 |
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