On the Asymptotic Behavior of Solutions of a Singular Cauchy Problem
We consider a singular Cauchy problem for a nonlinear differential equation unsolved with respect to the derivative of the unknown function. We prove the existence of continuously differentiable solutions, investigate their asymptotic behavior near the initial point, and determine their number.
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| Date: | 2001 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4337 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510466629959680 |
|---|---|
| author | Zernov, A. E. Meleshko, T. V. Зернов, А. Е. Мелешко, Т. В. Зернов, А. Е. Мелешко, Т. В. |
| author_facet | Zernov, A. E. Meleshko, T. V. Зернов, А. Е. Мелешко, Т. В. Зернов, А. Е. Мелешко, Т. В. |
| author_sort | Zernov, A. E. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:26:49Z |
| description | We consider a singular Cauchy problem for a nonlinear differential equation unsolved with respect to the derivative of the unknown function. We prove the existence of continuously differentiable solutions, investigate their asymptotic behavior near the initial point, and determine their number. |
| first_indexed | 2026-03-24T02:57:27Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4337 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:57:27Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/28/e912a7a67d3ed38a1c805f48eac03328.pdf |
| spelling | umjimathkievua-article-43372020-03-18T20:26:49Z On the Asymptotic Behavior of Solutions of a Singular Cauchy Problem Об асимптотическом поведении решений некоторой сингулярной задачи Коши Zernov, A. E. Meleshko, T. V. Зернов, А. Е. Мелешко, Т. В. Зернов, А. Е. Мелешко, Т. В. We consider a singular Cauchy problem for a nonlinear differential equation unsolved with respect to the derivative of the unknown function. We prove the existence of continuously differentiable solutions, investigate their asymptotic behavior near the initial point, and determine their number. Розглядається сингулярна задача Коші для нелінійного диференціального рівняння, не розв'язаного відносно похідної невідомої функції. Доведено існування неперервно диференційовних розв'язків, досліджено асимптотичну поведінку цих розв'язків навколо початкової точки та визначено їх кількість. Institute of Mathematics, NAS of Ukraine 2001-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4337 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 9 (2001); 1194-1203 Український математичний журнал; Том 53 № 9 (2001); 1194-1203 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4337/5378 https://umj.imath.kiev.ua/index.php/umj/article/view/4337/5379 Copyright (c) 2001 Zernov A. E.; Meleshko T. V. |
| spellingShingle | Zernov, A. E. Meleshko, T. V. Зернов, А. Е. Мелешко, Т. В. Зернов, А. Е. Мелешко, Т. В. On the Asymptotic Behavior of Solutions of a Singular Cauchy Problem |
| title | On the Asymptotic Behavior of Solutions of a Singular Cauchy Problem |
| title_alt | Об асимптотическом поведении решений некоторой сингулярной задачи Коши |
| title_full | On the Asymptotic Behavior of Solutions of a Singular Cauchy Problem |
| title_fullStr | On the Asymptotic Behavior of Solutions of a Singular Cauchy Problem |
| title_full_unstemmed | On the Asymptotic Behavior of Solutions of a Singular Cauchy Problem |
| title_short | On the Asymptotic Behavior of Solutions of a Singular Cauchy Problem |
| title_sort | on the asymptotic behavior of solutions of a singular cauchy problem |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4337 |
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