A resonance case of the existence of solutions of a quasilinear second-order differential system, which are represented by Fourier series with slowly varying parameters
For a quasilinear second-order differential system, whose coefficients have the form of Fourier series with slowly varying coefficients and frequency, we prove, under certain conditions, the existence of a particular solution having a similar structure. This result is obtained in the case where the...
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| Date: | 1999 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1999
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4612 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510760176713728 |
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| author | Shchegolev, S. A. Щеголев, С. А. Щеголев, С. А. |
| author_facet | Shchegolev, S. A. Щеголев, С. А. Щеголев, С. А. |
| author_sort | Shchegolev, S. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:09:38Z |
| description | For a quasilinear second-order differential system, whose coefficients have the form of Fourier series with slowly varying coefficients and frequency, we prove, under certain conditions, the existence of a particular solution having a similar structure. This result is obtained in the case where the characteristic equation possesses purely imaginary roots, which satisfy a certain resonance relation. |
| first_indexed | 2026-03-24T03:02:07Z |
| format | Article |
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| id | umjimathkievua-article-4612 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:02:07Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/5e/42c0027dd77c04ef694ad1fe01950b5e.pdf |
| spelling | umjimathkievua-article-46122020-03-18T21:09:38Z A resonance case of the existence of solutions of a quasilinear second-order differential system, which are represented by Fourier series with slowly varying parameters Резонансный случай существования решений квазилинейной дифференциальной системы второго порядка, представимых рядами Фурье, содержащими медленно меняющиеся параметры Shchegolev, S. A. Щеголев, С. А. Щеголев, С. А. For a quasilinear second-order differential system, whose coefficients have the form of Fourier series with slowly varying coefficients and frequency, we prove, under certain conditions, the existence of a particular solution having a similar structure. This result is obtained in the case where the characteristic equation possesses purely imaginary roots, which satisfy a certain resonance relation. Для квазілінійної диференціальної системи другого порядку, коефіцієнти якої мають вигляд рядів Фур'є з повільно змінними коефіцієнтами і частотою, при певних умовах доведено існування частинного розв'язку аналогічної структури у випадку суто уявних коренів характеристичного рівняння, які задовольняють деяке резонансне співвідношення. Institute of Mathematics, NAS of Ukraine 1999-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4612 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 2 (1999); 285–288 Український математичний журнал; Том 51 № 2 (1999); 285–288 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4612/5927 https://umj.imath.kiev.ua/index.php/umj/article/view/4612/5928 Copyright (c) 1999 Shchegolev S. A. |
| spellingShingle | Shchegolev, S. A. Щеголев, С. А. Щеголев, С. А. A resonance case of the existence of solutions of a quasilinear second-order differential system, which are represented by Fourier series with slowly varying parameters |
| title | A resonance case of the existence of solutions of a quasilinear second-order differential system, which are represented by Fourier series with slowly varying parameters |
| title_alt | Резонансный случай существования решений квазилинейной дифференциальной системы второго порядка, представимых рядами Фурье, содержащими медленно меняющиеся параметры |
| title_full | A resonance case of the existence of solutions of a quasilinear second-order differential system, which are represented by Fourier series with slowly varying parameters |
| title_fullStr | A resonance case of the existence of solutions of a quasilinear second-order differential system, which are represented by Fourier series with slowly varying parameters |
| title_full_unstemmed | A resonance case of the existence of solutions of a quasilinear second-order differential system, which are represented by Fourier series with slowly varying parameters |
| title_short | A resonance case of the existence of solutions of a quasilinear second-order differential system, which are represented by Fourier series with slowly varying parameters |
| title_sort | resonance case of the existence of solutions of a quasilinear second-order differential system, which are represented by fourier series with slowly varying parameters |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4612 |
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