On the Growth of Meromorphic Solutions of an Algebraic Differential Equation in a Neighborhood of a Logarithmic Singular Point
We prove that if an analytic function f with an isolated singular point at ∞ is a solution of the differential equation P(zlnz, f, f′) = 0, where P is a polynomial in all variables, then f has finite order. We study the asymptotic properties of a meromorphic solution with logarithmic singularity....
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| Datum: | 2003 |
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| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2003
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4019 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510150065913856 |
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| author | Mokhonko, A. Z. Мохонько, А. З. Мохонько, А. З. |
| author_facet | Mokhonko, A. Z. Мохонько, А. З. Мохонько, А. З. |
| author_sort | Mokhonko, A. Z. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:18:28Z |
| description | We prove that if an analytic function f with an isolated singular point at ∞ is a solution of the differential equation P(zlnz, f, f′) = 0, where P is a polynomial in all variables, then f has finite order. We study the asymptotic properties of a meromorphic solution with logarithmic singularity. |
| first_indexed | 2026-03-24T02:52:25Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4019 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:52:25Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/58/809e591091d72055d868b955c6d84b58.pdf |
| spelling | umjimathkievua-article-40192020-03-18T20:18:28Z On the Growth of Meromorphic Solutions of an Algebraic Differential Equation in a Neighborhood of a Logarithmic Singular Point О возрастании мероморфных решений алгебраического дифференциального уравнения в окрестности логарифмической особой точки Mokhonko, A. Z. Мохонько, А. З. Мохонько, А. З. We prove that if an analytic function f with an isolated singular point at ∞ is a solution of the differential equation P(zlnz, f, f′) = 0, where P is a polynomial in all variables, then f has finite order. We study the asymptotic properties of a meromorphic solution with logarithmic singularity. Доведено, що коли аналітична функція / з ізольованою особливою точкою у є розв'язком диференціального рівняння $P(zlnz, f, f′) = 0 $ ($Р$ — многочлен по всіх змінних), то $f$ має скінченний порядок. Вивчаються асимптотичні властивості мероморфного розв'язку із логарифмічною особливою точкою. Institute of Mathematics, NAS of Ukraine 2003-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4019 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 11 (2003); 1489-1502 Український математичний журнал; Том 55 № 11 (2003); 1489-1502 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4019/4749 https://umj.imath.kiev.ua/index.php/umj/article/view/4019/4750 Copyright (c) 2003 Mokhonko A. Z. |
| spellingShingle | Mokhonko, A. Z. Мохонько, А. З. Мохонько, А. З. On the Growth of Meromorphic Solutions of an Algebraic Differential Equation in a Neighborhood of a Logarithmic Singular Point |
| title | On the Growth of Meromorphic Solutions of an Algebraic Differential Equation in a Neighborhood of a Logarithmic Singular Point |
| title_alt | О возрастании мероморфных решений алгебраического дифференциального уравнения в окрестности логарифмической особой точки |
| title_full | On the Growth of Meromorphic Solutions of an Algebraic Differential Equation in a Neighborhood of a Logarithmic Singular Point |
| title_fullStr | On the Growth of Meromorphic Solutions of an Algebraic Differential Equation in a Neighborhood of a Logarithmic Singular Point |
| title_full_unstemmed | On the Growth of Meromorphic Solutions of an Algebraic Differential Equation in a Neighborhood of a Logarithmic Singular Point |
| title_short | On the Growth of Meromorphic Solutions of an Algebraic Differential Equation in a Neighborhood of a Logarithmic Singular Point |
| title_sort | on the growth of meromorphic solutions of an algebraic differential equation in a neighborhood of a logarithmic singular point |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4019 |
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