Qualitative Investigation of the Singular Cauchy Problem $\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0}$
We prove the existence of continuously differentiable solutions $x:(0,ρ] → R$ with required asymptotic properties as $t → +0$ and determine the number of these solutions.
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| Дата: | 2003 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2003
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4010 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510140040478720 |
|---|---|
| author | Zernov, A. E. Зернов, А. Е. Зернов, А. Е. |
| author_facet | Zernov, A. E. Зернов, А. Е. Зернов, А. Е. |
| author_sort | Zernov, A. E. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:18:09Z |
| description | We prove the existence of continuously differentiable solutions $x:(0,ρ] → R$ with required asymptotic properties as $t → +0$ and determine the number of these solutions. |
| first_indexed | 2026-03-24T02:52:15Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4010 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:52:15Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/f5/aa443fa51504bdb53d1a9280242393f5.pdf |
| spelling | umjimathkievua-article-40102020-03-18T20:18:09Z Qualitative Investigation of the Singular Cauchy Problem $\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0}$ Качественное исследование сингулярной задачи Коши $\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0}$ Zernov, A. E. Зернов, А. Е. Зернов, А. Е. We prove the existence of continuously differentiable solutions $x:(0,ρ] → R$ with required asymptotic properties as $t → +0$ and determine the number of these solutions. Доведено існування неперервно диференційовних розв'язків $x:(0,ρ] → R$ з потрібними асимптотичними властивостями при $t → +0$ та визначено кількість цих розв'язків. Institute of Mathematics, NAS of Ukraine 2003-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4010 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 10 (2003); 1419-1424 Український математичний журнал; Том 55 № 10 (2003); 1419-1424 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4010/4732 https://umj.imath.kiev.ua/index.php/umj/article/view/4010/4733 Copyright (c) 2003 Zernov A. E. |
| spellingShingle | Zernov, A. E. Зернов, А. Е. Зернов, А. Е. Qualitative Investigation of the Singular Cauchy Problem $\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0}$ |
| title | Qualitative Investigation of the Singular Cauchy Problem
$\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0}$ |
| title_alt | Качественное исследование сингулярной задачи Коши
$\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0}$ |
| title_full | Qualitative Investigation of the Singular Cauchy Problem
$\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0}$ |
| title_fullStr | Qualitative Investigation of the Singular Cauchy Problem
$\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0}$ |
| title_full_unstemmed | Qualitative Investigation of the Singular Cauchy Problem
$\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0}$ |
| title_short | Qualitative Investigation of the Singular Cauchy Problem
$\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0}$ |
| title_sort | qualitative investigation of the singular cauchy problem
$\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0}$ |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4010 |
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