Estimation of the solutions of the Sturm-Liouville equation
Exact estimates are presented for the solutions of the problem $\ddot y + \lambda ^2 p(t)y = 0, y(0) = 0, \dot y(0) = 1$ with $p(t)$ satisfying one of the following conditions: $$(i) |p(t)| \leqslant M< \infty ; (ii) 0< \omega _1 \leqslant p(t) \leqslant \omega _2< \infty...
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| Datum: | 1994 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1994
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5760 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511988610760704 |
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| author | Levin, B. Ya. Mirochnik, L. Ya. Левин, Б. Я. Мирочник, Л. Я. Левин, Б. Я. Мирочник, Л. Я. |
| author_facet | Levin, B. Ya. Mirochnik, L. Ya. Левин, Б. Я. Мирочник, Л. Я. Левин, Б. Я. Мирочник, Л. Я. |
| author_sort | Levin, B. Ya. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:17:07Z |
| description | Exact estimates are presented for the solutions of the problem $\ddot y + \lambda ^2 p(t)y = 0, y(0) = 0, \dot y(0) = 1$ with $p(t)$ satisfying one of the following conditions:
$$(i) |p(t)| \leqslant M< \infty ; (ii) 0< \omega _1 \leqslant p(t) \leqslant \omega _2< \infty ; (iii) \mathop {sup}\limits_x \int_x^{x + T} {p(t)dt = P_T /T.}$$
The extremal solutions are found. |
| first_indexed | 2026-03-24T03:21:38Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5760 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:21:38Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/e3/d17052b1be0a0a43b8fe87078ba994e3.pdf |
| spelling | umjimathkievua-article-57602020-03-19T09:17:07Z Estimation of the solutions of the Sturm-Liouville equation Об оценках решений уравнения Штурма - Лиувилля Levin, B. Ya. Mirochnik, L. Ya. Левин, Б. Я. Мирочник, Л. Я. Левин, Б. Я. Мирочник, Л. Я. Exact estimates are presented for the solutions of the problem $\ddot y + \lambda ^2 p(t)y = 0, y(0) = 0, \dot y(0) = 1$ with $p(t)$ satisfying one of the following conditions: $$(i) |p(t)| \leqslant M< \infty ; (ii) 0< \omega _1 \leqslant p(t) \leqslant \omega _2< \infty ; (iii) \mathop {sup}\limits_x \int_x^{x + T} {p(t)dt = P_T /T.}$$ The extremal solutions are found. Наведені точні оцінки розв’язків задачі $\ddot y + \lambda ^2 p(t)y = 0, y(0) = 0, \dot y(0) = 1$ при $p(t)$, що задовольняє одну із умов $$(i) |p(t)| \leqslant M< \infty ; (ii) 0< \omega _1 \leqslant p(t) \leqslant \omega _2< \infty ; (iii) \mathop {sup}\limits_x \int_x^{x + T} {p(t)dt = P_T /T.}$$ Знайдені екстремальні розв’язки. Institute of Mathematics, NAS of Ukraine 1994-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5760 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 3 (1994); 244–278 Український математичний журнал; Том 46 № 3 (1994); 244–278 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5760/8204 https://umj.imath.kiev.ua/index.php/umj/article/view/5760/8205 Copyright (c) 1994 Levin B. Ya.; Mirochnik L. Ya. |
| spellingShingle | Levin, B. Ya. Mirochnik, L. Ya. Левин, Б. Я. Мирочник, Л. Я. Левин, Б. Я. Мирочник, Л. Я. Estimation of the solutions of the Sturm-Liouville equation |
| title | Estimation of the solutions of the Sturm-Liouville equation |
| title_alt | Об оценках решений уравнения Штурма - Лиувилля |
| title_full | Estimation of the solutions of the Sturm-Liouville equation |
| title_fullStr | Estimation of the solutions of the Sturm-Liouville equation |
| title_full_unstemmed | Estimation of the solutions of the Sturm-Liouville equation |
| title_short | Estimation of the solutions of the Sturm-Liouville equation |
| title_sort | estimation of the solutions of the sturm-liouville equation |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5760 |
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