Estimates of eigenvalues of self-adjoint boundary-value problems with periodic coefficients
We consider self-adjoint boundary-value problems with discrete spectrum and coefficients periodic in a certain coordinate. We establish upper bounds for eigenvalues in terms of the eigenvalues of the corresponding problem with averaged coefficients. We illustrate the results obtained in the case of...
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| Datum: | 1998 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1998
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4901 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511082070671360 |
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| author | Zevin, A. A. Зевин, А. А. Зевин, А. А. |
| author_facet | Zevin, A. A. Зевин, А. А. Зевин, А. А. |
| author_sort | Zevin, A. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:16:53Z |
| description | We consider self-adjoint boundary-value problems with discrete spectrum and coefficients periodic in a certain coordinate. We establish upper bounds for eigenvalues in terms of the eigenvalues of the corresponding problem with averaged coefficients. We illustrate the results obtained in the case of the Hill vector equation and for circular and rectangular plates with periodic coefficients. |
| first_indexed | 2026-03-24T03:07:14Z |
| format | Article |
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| id | umjimathkievua-article-4901 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:07:14Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ef/e3fd88bd7dda7fa442f3c57a7c2e0fef.pdf |
| spelling | umjimathkievua-article-49012020-03-18T21:16:53Z Estimates of eigenvalues of self-adjoint boundary-value problems with periodic coefficients Оценки собственных значений самосопряженных краевых задач с периодическими коэффициентами Zevin, A. A. Зевин, А. А. Зевин, А. А. We consider self-adjoint boundary-value problems with discrete spectrum and coefficients periodic in a certain coordinate. We establish upper bounds for eigenvalues in terms of the eigenvalues of the corresponding problem with averaged coefficients. We illustrate the results obtained in the case of the Hill vector equation and for circular and rectangular plates with periodic coefficients. Розглядаються самоспряжені крайові задачі з дискретним спектром, коефіцієнти яких періодичні за деякою координатою. Знайдені верхні оцінки власних значень, виражені через власні значення відповідної задачі з осередпепими коефіцієнтами. Результати ілюструються на прикладі векторного рівняння Хілла, круглої та прямокутної пластинки з періодичними коефіцієнтами. Institute of Mathematics, NAS of Ukraine 1998-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4901 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 5 (1998); 632–638 Український математичний журнал; Том 50 № 5 (1998); 632–638 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4901/6501 https://umj.imath.kiev.ua/index.php/umj/article/view/4901/6502 Copyright (c) 1998 Zevin A. A. |
| spellingShingle | Zevin, A. A. Зевин, А. А. Зевин, А. А. Estimates of eigenvalues of self-adjoint boundary-value problems with periodic coefficients |
| title | Estimates of eigenvalues of self-adjoint boundary-value problems with periodic coefficients |
| title_alt | Оценки собственных значений самосопряженных краевых задач с периодическими коэффициентами |
| title_full | Estimates of eigenvalues of self-adjoint boundary-value problems with periodic coefficients |
| title_fullStr | Estimates of eigenvalues of self-adjoint boundary-value problems with periodic coefficients |
| title_full_unstemmed | Estimates of eigenvalues of self-adjoint boundary-value problems with periodic coefficients |
| title_short | Estimates of eigenvalues of self-adjoint boundary-value problems with periodic coefficients |
| title_sort | estimates of eigenvalues of self-adjoint boundary-value problems with periodic coefficients |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4901 |
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