Some approaches to the construction of approximate solutions of the generalized Goursat problem for systems of certain quasilinear partial differential equations with deviating argument
We construct and investigate monotone and alternating rapidly convergent two-sided methods for the approximate integration of the generalized Goursat problem, prove the existence and uniqueness of its regular solution, establish theorems on differential inequality and comparison, and obtain sufficie...
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| Date: | 1995 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1995
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5560 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511790148878336 |
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| author | Marynetz, V. V. Маринець, В. В. |
| author_facet | Marynetz, V. V. Маринець, В. В. |
| author_sort | Marynetz, V. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:13:33Z |
| description | We construct and investigate monotone and alternating rapidly convergent two-sided methods for the approximate integration of the generalized Goursat problem, prove the existence and uniqueness of its regular solution, establish theorems on differential inequality and comparison, and obtain sufficient conditions for the existence of solutions of the indicated problem of fixed sign in a given domain. |
| first_indexed | 2026-03-24T03:18:29Z |
| format | Article |
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| id | umjimathkievua-article-5560 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:18:29Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/f5/1e8f6926ff7cb1146b0e177fe3bea9f5.pdf |
| spelling | umjimathkievua-article-55602020-03-19T09:13:33Z Some approaches to the construction of approximate solutions of the generalized Goursat problem for systems of certain quasilinear partial differential equations with deviating argument Деякі підходи побудови наближеного розв’язку узагальненої задачі Гурса для систем визначених квазілінійних диференціальних рівнянь з частинними похідними з аргументом, що відхиляється Marynetz, V. V. Маринець, В. В. We construct and investigate monotone and alternating rapidly convergent two-sided methods for the approximate integration of the generalized Goursat problem, prove the existence and uniqueness of its regular solution, establish theorems on differential inequality and comparison, and obtain sufficient conditions for the existence of solutions of the indicated problem of fixed sign in a given domain. Побудовано і досліджено монотонні та альтернуючі швидкозбіжні двосторонні методи наближеного інтегрування узагальненої задачі Гурса, доведено існування та єдиність її регулярного розв’язку, теореми про диференціальну нерівність, порівняння, одержано достатні умови існування знакосталих розв’язків вказаної задачі в розглядуваній області. Institute of Mathematics, NAS of Ukraine 1995-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5560 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 12 (1995); 1667–1675 Український математичний журнал; Том 47 № 12 (1995); 1667–1675 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5560/7808 https://umj.imath.kiev.ua/index.php/umj/article/view/5560/7809 Copyright (c) 1995 Marynetz V. V. |
| spellingShingle | Marynetz, V. V. Маринець, В. В. Some approaches to the construction of approximate solutions of the generalized Goursat problem for systems of certain quasilinear partial differential equations with deviating argument |
| title | Some approaches to the construction of approximate solutions of the generalized Goursat problem for systems of certain quasilinear partial differential equations with deviating argument |
| title_alt | Деякі підходи побудови наближеного розв’язку узагальненої задачі Гурса для систем визначених квазілінійних диференціальних рівнянь з частинними похідними з аргументом, що відхиляється |
| title_full | Some approaches to the construction of approximate solutions of the generalized Goursat problem for systems of certain quasilinear partial differential equations with deviating argument |
| title_fullStr | Some approaches to the construction of approximate solutions of the generalized Goursat problem for systems of certain quasilinear partial differential equations with deviating argument |
| title_full_unstemmed | Some approaches to the construction of approximate solutions of the generalized Goursat problem for systems of certain quasilinear partial differential equations with deviating argument |
| title_short | Some approaches to the construction of approximate solutions of the generalized Goursat problem for systems of certain quasilinear partial differential equations with deviating argument |
| title_sort | some approaches to the construction of approximate solutions of the generalized goursat problem for systems of certain quasilinear partial differential equations with deviating argument |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5560 |
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