On asymptotics of solutions of one Cauchy’s problem
We consider the Cauchy problem $(x')^n=at^r+bx+f(t,x,x'), x(0)=0$. We prove the existence of continuously differentiable solutions and study their asymptotic behavior for $t→+0$.
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| Date: | 2025 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2025
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9355 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513507362996224 |
|---|---|
| author | Zernov , A. E. Зернов , А. Е. |
| author_facet | Zernov , A. E. Зернов , А. Е. |
| author_sort | Zernov , A. E. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-06-30T14:20:55Z |
| description | We consider the Cauchy problem $(x')^n=at^r+bx+f(t,x,x'), x(0)=0$. We prove the existence of continuously differentiable solutions and study their asymptotic behavior for $t→+0$. |
| first_indexed | 2026-03-24T03:45:47Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-9355 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:45:47Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/79/27df4e145e5830a8e8f62c5dc3dedd79.pdf |
| spelling | umjimathkievua-article-93552025-06-30T14:20:55Z On asymptotics of solutions of one Cauchy’s problem Об асимптотике решении одной задачи Коши Zernov , A. E. Зернов , А. Е. - We consider the Cauchy problem $(x')^n=at^r+bx+f(t,x,x'), x(0)=0$. We prove the existence of continuously differentiable solutions and study their asymptotic behavior for $t→+0$. Рассматривается задача Коши $(x')^n=at^r+bx+f(t,x,x'), x(0)=0$. Доказано существование непрерывно дифферецируемых решений, исследовано их асимптотическое поведение при $t→+0$. Розглядається задача Коші $(x')^n=at^r+bx+f(t,x,x'), x(0)=0$. Доведено існування неперервно диференційовних розв'язків, досліджена їх асимптотична поведінка при $t→+0$. Institute of Mathematics, NAS of Ukraine 2025-06-30 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/9355 Ukrains’kyi Matematychnyi Zhurnal; Vol. 43 No. 2 (1991); 187-193 Український математичний журнал; Том 43 № 2 (1991); 187-193 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/9355/10505 Copyright (c) 2025 А. Е. Зернов |
| spellingShingle | Zernov , A. E. Зернов , А. Е. On asymptotics of solutions of one Cauchy’s problem |
| title | On asymptotics of solutions of one Cauchy’s problem |
| title_alt | Об асимптотике решении одной задачи Коши |
| title_full | On asymptotics of solutions of one Cauchy’s problem |
| title_fullStr | On asymptotics of solutions of one Cauchy’s problem |
| title_full_unstemmed | On asymptotics of solutions of one Cauchy’s problem |
| title_short | On asymptotics of solutions of one Cauchy’s problem |
| title_sort | on asymptotics of solutions of one cauchy’s problem |
| topic_facet | - |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9355 |
| work_keys_str_mv | AT zernovae onasymptoticsofsolutionsofonecauchysproblem AT zernovae onasymptoticsofsolutionsofonecauchysproblem AT zernovae obasimptotikerešeniiodnojzadačikoši AT zernovae obasimptotikerešeniiodnojzadačikoši |