Meromorphous solutions of algebraic differential equations in angular regions
We obtain asymptotic estimates of meromorphic solutions to the differential equation Pn(z, w, wʹ) =Pn-1(z, w, wʹ,...,wm) in the angular domain Р={z: α ≤ argz ≤ β}. Here Pn(z, w, wʹ) is a polynomial in all variables, and of degree n with respect to w and w′; Pn-1(z, w, wʹ,...,wm) is a polynomial in a...
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| Date: | 1992 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
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Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7893 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512806807273472 |
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| author | Mokhonko , A. Z. Мохонько , А. З. |
| author_facet | Mokhonko , A. Z. Мохонько , А. З. |
| author_sort | Mokhonko , A. Z. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-10-26T11:41:49Z |
| description | We obtain asymptotic estimates of meromorphic solutions to the differential equation Pn(z, w, wʹ) =Pn-1(z, w, wʹ,...,wm) in the angular domain Р={z: α ≤ argz ≤ β}. Here Pn(z, w, wʹ) is a polynomial in all variables, and of degree n with respect to w and w′; Pn-1(z, w, wʹ,...,wm) is a polynomial in all variables, and of degree ≤ n −1 with respect to w, wʹ,...,wm. In the particular case, when the solutions are entire functions, these estimates are more precise than the known estimates that are obtained by using the method of Wiman-Valiron, which cannot be applied to meromorphic solutions in the domain P. |
| first_indexed | 2026-03-24T03:34:39Z |
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| id | umjimathkievua-article-7893 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:34:39Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/3c/ebaf06f8abe8832c2058a580a28f013c.pdf |
| spelling | umjimathkievua-article-78932023-10-26T11:41:49Z Meromorphous solutions of algebraic differential equations in angular regions О мероморфных решениях алгебраических дифференциальных уравнений в угловых областях Mokhonko , A. Z. Мохонько , А. З. We obtain asymptotic estimates of meromorphic solutions to the differential equation Pn(z, w, wʹ) =Pn-1(z, w, wʹ,...,wm) in the angular domain Р={z: α ≤ argz ≤ β}. Here Pn(z, w, wʹ) is a polynomial in all variables, and of degree n with respect to w and w′; Pn-1(z, w, wʹ,...,wm) is a polynomial in all variables, and of degree ≤ n −1 with respect to w, wʹ,...,wm. In the particular case, when the solutions are entire functions, these estimates are more precise than the known estimates that are obtained by using the method of Wiman-Valiron, which cannot be applied to meromorphic solutions in the domain P. Получены асимптотические оценки мероморфных в угловой области Р={z: α ≤ argz ≤ β} решений дифференциального уравнения Pn(z, w, wʹ) =Pn-1(z, w, wʹ,...,wm), Pn(z, w, wʹ) — многочлен по всем переменным степени n относительно w и wʹ; Pn-1(z, w, wʹ,...,wm) —многочлен по всем переменным степени ≤ n −1 относительно w, wʹ,...,wm. В частном случае целых решенйй эти оценки уточняют известные, получаемые методом Вимана—Валнрона, который не применим к мероморфным в области Р решениям. Одержані асимптотичні оцінки мероморфних у кутовій області Р={z: α ≤ argz ≤ β} розв’язків диференціального рівняння Pn(z, w, wʹ) =Pn-1(z, w, wʹ,...,wm), Pn(z, w, wʹ) —многочлен по всіх змінних степеня n відносно w та wʹ; Pn-1(z, w, wʹ,...,wm) многочлен по всіх змінних степеня ≤ n −1 відносно w, wʹ,...,wm. В окремому випадку цілих розв’язків ці оцінки уточнюють відомі, що одержуються методом Вімана — Валірона, який не можна застосувати до мероморфних в області Р розв’язків. Institute of Mathematics, NAS of Ukraine 1992-04-17 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7893 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 4 (1992); 514-523 Український математичний журнал; Том 44 № 4 (1992); 514-523 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/7893/9513 Copyright (c) 1992 A. Z. Mokhonko |
| spellingShingle | Mokhonko , A. Z. Мохонько , А. З. Meromorphous solutions of algebraic differential equations in angular regions |
| title | Meromorphous solutions of algebraic differential equations in angular regions |
| title_alt | О мероморфных решениях алгебраических дифференциальных уравнений в угловых областях |
| title_full | Meromorphous solutions of algebraic differential equations in angular regions |
| title_fullStr | Meromorphous solutions of algebraic differential equations in angular regions |
| title_full_unstemmed | Meromorphous solutions of algebraic differential equations in angular regions |
| title_short | Meromorphous solutions of algebraic differential equations in angular regions |
| title_sort | meromorphous solutions of algebraic differential equations in angular regions |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7893 |
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