A Problem with Nonlocal Conditions for Partial Differential Equations with Variable Coefficients
We establish conditions for the unique solvability of a problem for partial differential equations with coefficients dependent on variables t and x in a rectangular domain with nonlocal two-point conditions with respect to t and local boundary conditions with respect to x. We prove metric statements...
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| Date: | 2001 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4352 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510482627035136 |
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| author | Vlasii, O. D. Ptashnik, B. I. Власій, О. Д. Пташник, Б. Й. |
| author_facet | Vlasii, O. D. Ptashnik, B. I. Власій, О. Д. Пташник, Б. Й. |
| author_sort | Vlasii, O. D. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:27:17Z |
| description | We establish conditions for the unique solvability of a problem for partial differential equations with coefficients dependent on variables t and x in a rectangular domain with nonlocal two-point conditions with respect to t and local boundary conditions with respect to x. We prove metric statements related to lower bounds of small denominators appearing in the course of solution of the problem. |
| first_indexed | 2026-03-24T02:57:42Z |
| format | Article |
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| id | umjimathkievua-article-4352 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:57:42Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/90/b5ea08fa3538d422a6acc27af7f2eb90.pdf |
| spelling | umjimathkievua-article-43522020-03-18T20:27:17Z A Problem with Nonlocal Conditions for Partial Differential Equations with Variable Coefficients Задача з нелокальними умовами для рівнянь із частинними похідними зі змінними коефіцієнтами Vlasii, O. D. Ptashnik, B. I. Власій, О. Д. Пташник, Б. Й. We establish conditions for the unique solvability of a problem for partial differential equations with coefficients dependent on variables t and x in a rectangular domain with nonlocal two-point conditions with respect to t and local boundary conditions with respect to x. We prove metric statements related to lower bounds of small denominators appearing in the course of solution of the problem. Встановлено умови однозначної розв'язності задачі з нелокальними двоточковими умовами за змінною $t$ та локальними крайовими умовами за змінною $х$ для диференціальних рівнянь із частинними похідними зі змінними по $t$ та $х$ коефіцієнтами у прямокутній області. Доведено метричні твердження, які стосуються оцінок знизу малих знаменників, що виникають при побудові розв'язку задачі. Institute of Mathematics, NAS of Ukraine 2001-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4352 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 10 (2001); 1328-1336 Український математичний журнал; Том 53 № 10 (2001); 1328-1336 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4352/5408 https://umj.imath.kiev.ua/index.php/umj/article/view/4352/5409 Copyright (c) 2001 Vlasii O. D.; Ptashnik B. I. |
| spellingShingle | Vlasii, O. D. Ptashnik, B. I. Власій, О. Д. Пташник, Б. Й. A Problem with Nonlocal Conditions for Partial Differential Equations with Variable Coefficients |
| title | A Problem with Nonlocal Conditions for Partial Differential Equations with Variable Coefficients |
| title_alt | Задача з нелокальними умовами для рівнянь із частинними похідними зі змінними коефіцієнтами |
| title_full | A Problem with Nonlocal Conditions for Partial Differential Equations with Variable Coefficients |
| title_fullStr | A Problem with Nonlocal Conditions for Partial Differential Equations with Variable Coefficients |
| title_full_unstemmed | A Problem with Nonlocal Conditions for Partial Differential Equations with Variable Coefficients |
| title_short | A Problem with Nonlocal Conditions for Partial Differential Equations with Variable Coefficients |
| title_sort | problem with nonlocal conditions for partial differential equations with variable coefficients |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4352 |
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