On the Order of Growth of the Solutions of Linear Differential Equations in the Vicinity of a Branching Point
Assume that the coefficients and solutions of the equation $f^{(n)}+p_{n−1}(z)f^{(n−1)} +...+ p_{s+1}(z)f^{(s+1)} +...+ p_0(z)f = 0$ have a branching point at infinity (e.g., a logarithmic singularity) and that the coefficients $p_j , j = s+1, . . . ,n−1$, increase slower (in terms of the Nevanlinna...
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| Datum: | 2015 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2015
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1969 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860507862210445312 |
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| author | Mokhonko, A. Z. Mokhonko, A. A. Мохонько, А. З. Мохонько, А. А. Мохонько, А. З. Мохонько, А. А. |
| author_facet | Mokhonko, A. Z. Mokhonko, A. A. Мохонько, А. З. Мохонько, А. А. Мохонько, А. З. Мохонько, А. А. |
| author_sort | Mokhonko, A. Z. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2019-12-05T09:47:39Z |
| description | Assume that the coefficients and solutions of the equation $f^{(n)}+p_{n−1}(z)f^{(n−1)} +...+ p_{s+1}(z)f^{(s+1)} +...+ p_0(z)f = 0$ have a branching point at infinity (e.g., a logarithmic singularity) and that the coefficients $p_j , j = s+1, . . . ,n−1$, increase slower (in terms of the Nevanlinna characteristics) than $p_s(z)$. It is proved that this equation has at most $s$ linearly independent solutions of finite order. |
| first_indexed | 2026-03-24T02:16:03Z |
| format | Article |
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| id | umjimathkievua-article-1969 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T02:16:03Z |
| publishDate | 2015 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-19692019-12-05T09:47:39Z On the Order of Growth of the Solutions of Linear Differential Equations in the Vicinity of a Branching Point О порядке роста решений линейных дифференциальных уравнений в окрестности точки ветвления Mokhonko, A. Z. Mokhonko, A. A. Мохонько, А. З. Мохонько, А. А. Мохонько, А. З. Мохонько, А. А. Assume that the coefficients and solutions of the equation $f^{(n)}+p_{n−1}(z)f^{(n−1)} +...+ p_{s+1}(z)f^{(s+1)} +...+ p_0(z)f = 0$ have a branching point at infinity (e.g., a logarithmic singularity) and that the coefficients $p_j , j = s+1, . . . ,n−1$, increase slower (in terms of the Nevanlinna characteristics) than $p_s(z)$. It is proved that this equation has at most $s$ linearly independent solutions of finite order. Доказано, что если в уравнении $f^{(n)}+p_{n−1}(z)f^{(n−1)} +...+ p_{s+1}(z)f^{(s+1)} +...+ p_0(z)f = 0$ коэффициенты и решения имеют точку ветвления на бесконечности (например, логарифмическая особенность) и что коэффициенты $p_j , j = s+1, . . . ,n−1$ возрастают медленнее (с точки зрения характеристик неванлинновских), чем $p_s(z)$, то это уравнение имеет не более $s$ линейно независимых решений конечного порядка. Institute of Mathematics, NAS of Ukraine 2015-01-25 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/1969 Ukrains’kyi Matematychnyi Zhurnal; Vol. 67 No. 1 (2015); 139-144 Український математичний журнал; Том 67 № 1 (2015); 139-144 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/1969/960 Copyright (c) 2015 Mokhonko A. Z.; Mokhonko A. A. |
| spellingShingle | Mokhonko, A. Z. Mokhonko, A. A. Мохонько, А. З. Мохонько, А. А. Мохонько, А. З. Мохонько, А. А. On the Order of Growth of the Solutions of Linear Differential Equations in the Vicinity of a Branching Point |
| title | On the Order of Growth of the Solutions of Linear Differential Equations in the Vicinity of a Branching Point |
| title_alt | О порядке роста решений линейных дифференциальных
уравнений в окрестности точки ветвления |
| title_full | On the Order of Growth of the Solutions of Linear Differential Equations in the Vicinity of a Branching Point |
| title_fullStr | On the Order of Growth of the Solutions of Linear Differential Equations in the Vicinity of a Branching Point |
| title_full_unstemmed | On the Order of Growth of the Solutions of Linear Differential Equations in the Vicinity of a Branching Point |
| title_short | On the Order of Growth of the Solutions of Linear Differential Equations in the Vicinity of a Branching Point |
| title_sort | on the order of growth of the solutions of linear differential equations in the vicinity of a branching point |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/1969 |
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