Construction of Asymptotic Solutions of Linear Systems of Differential Equations with Two Small Parameters
We consider a linear homogeneous system of differential equations with two small parameters. In this system, the dependence on one parameter is regular and on the other is singular. Using methods of the theory of perturbations of linear operators and a space analog of the Newton diagrams, we investi...
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| Date: | 2003 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2003
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3971 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510103512285184 |
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| author | Yakovets, V. P. Яковець, В. П. |
| author_facet | Yakovets, V. P. Яковець, В. П. |
| author_sort | Yakovets, V. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:17:28Z |
| description | We consider a linear homogeneous system of differential equations with two small parameters. In this system, the dependence on one parameter is regular and on the other is singular. Using methods of the theory of perturbations of linear operators and a space analog of the Newton diagrams, we investigate the asymptotics of a general solution of this system in the case where its leading matrix has a multiple eigenvalue associated with a multiple elementary divisor. |
| first_indexed | 2026-03-24T02:51:41Z |
| format | Article |
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| id | umjimathkievua-article-3971 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:51:41Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ce/0c01c1f871e8c1343bd8fd2e01f5e8ce.pdf |
| spelling | umjimathkievua-article-39712020-03-18T20:17:28Z Construction of Asymptotic Solutions of Linear Systems of Differential Equations with Two Small Parameters Побудова асимптотичних розв'язків лінійних систем диференціальних рівнянь з двома малими параметрами Yakovets, V. P. Яковець, В. П. We consider a linear homogeneous system of differential equations with two small parameters. In this system, the dependence on one parameter is regular and on the other is singular. Using methods of the theory of perturbations of linear operators and a space analog of the Newton diagrams, we investigate the asymptotics of a general solution of this system in the case where its leading matrix has a multiple eigenvalue associated with a multiple elementary divisor. Розглянуто лінійну однорідну систему диференціальних рінпяпь з двома малими параметрами, у якій залежність під одного параметра є регулярною, а під другого — сингулярною. За допомогою методі» теорії збурень лінійних операторів та просторового аналогу діаграм Ньютона досліджено асимптотику загального розв'язку такої системи у випадку, коли її головна матриця має кратне власне значення, якому відповідає кратний елементарний дільник. Institute of Mathematics, NAS of Ukraine 2003-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3971 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 7 (2003); 961-976 Український математичний журнал; Том 55 № 7 (2003); 961-976 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3971/4654 https://umj.imath.kiev.ua/index.php/umj/article/view/3971/4655 Copyright (c) 2003 Yakovets V. P. |
| spellingShingle | Yakovets, V. P. Яковець, В. П. Construction of Asymptotic Solutions of Linear Systems of Differential Equations with Two Small Parameters |
| title | Construction of Asymptotic Solutions of Linear Systems of Differential Equations with Two Small Parameters |
| title_alt | Побудова асимптотичних розв'язків лінійних систем диференціальних рівнянь з двома малими параметрами |
| title_full | Construction of Asymptotic Solutions of Linear Systems of Differential Equations with Two Small Parameters |
| title_fullStr | Construction of Asymptotic Solutions of Linear Systems of Differential Equations with Two Small Parameters |
| title_full_unstemmed | Construction of Asymptotic Solutions of Linear Systems of Differential Equations with Two Small Parameters |
| title_short | Construction of Asymptotic Solutions of Linear Systems of Differential Equations with Two Small Parameters |
| title_sort | construction of asymptotic solutions of linear systems of differential equations with two small parameters |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3971 |
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