Distribution of eigenvalues of the Sturm-Liouville problem with slowly increasing potential
We establish an asymptotic representation of the function \(\tilde n(R) = \int\limits_0^R {\frac{{n(r) - n(0)}}{r}dr, R \in \Re } \subseteq [0, \infty ), R \to \infty ,\) where n(r) is the number of eigenvalues of the Sturm-Liouville problem on [0,∞) in (λ:¦λ¦≤r) (counting multiplicities). This...
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| Дата: | 1996 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1996
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5281 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511501846052864 |
|---|---|
| author | Palyutkin, V. G. Палюткин, В. Г. Палюткин, В. Г. |
| author_facet | Palyutkin, V. G. Палюткин, В. Г. Палюткин, В. Г. |
| author_sort | Palyutkin, V. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:29:27Z |
| description | We establish an asymptotic representation of the function \(\tilde n(R) = \int\limits_0^R {\frac{{n(r) - n(0)}}{r}dr, R \in \Re } \subseteq [0, \infty ), R \to \infty ,\) where n(r) is the number of eigenvalues of the Sturm-Liouville problem on [0,∞) in (λ:¦λ¦≤r) (counting multiplicities). This result is obtained under assumption that q(x) slowly (not faster than In x) increases to infinity as x→∞ and satisfies additional requirements on some intervals \([x_ - (R), x_ + (R)],R \in \Re \) . |
| first_indexed | 2026-03-24T03:13:54Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5281 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:13:54Z |
| publishDate | 1996 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/e6/3feb83d33aae2ec26c0a937cd4bbe9e6.pdf |
| spelling | umjimathkievua-article-52812020-03-18T21:29:27Z Distribution of eigenvalues of the Sturm-Liouville problem with slowly increasing potential Распределение собственных значений задачи Штурма - Лиувилля с медленно растущим потенциалом Palyutkin, V. G. Палюткин, В. Г. Палюткин, В. Г. We establish an asymptotic representation of the function \(\tilde n(R) = \int\limits_0^R {\frac{{n(r) - n(0)}}{r}dr, R \in \Re } \subseteq [0, \infty ), R \to \infty ,\) where n(r) is the number of eigenvalues of the Sturm-Liouville problem on [0,∞) in (λ:¦λ¦≤r) (counting multiplicities). This result is obtained under assumption that q(x) slowly (not faster than In x) increases to infinity as x→∞ and satisfies additional requirements on some intervals \([x_ - (R), x_ + (R)],R \in \Re \) . Встановлено асимптотичне зображення функції $$\tilde n(R) = \int\limits_0^R {\frac{{n(r) - n(0)}}{r}dr, R \in \Re } \subseteq [0, \infty ), R \to \infty ,$$ де $n(r)$ — кількість власних значень в $(λ: ¦λ¦ ≤ r)$ (з урахуванням кратності) задачі Штурма -Ліувілля на $[0,∞)$ у припущенні, що $q(x) → ∞ $ повільно (не швидше $\text{In} x$), коли $x → ∞ $, і задовольняє додаткові умови на певних інтервалах $[x_{ -} (R), x_{ +} (R)],R \in \Re$. Institute of Mathematics, NAS of Ukraine 1996-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5281 Ukrains’kyi Matematychnyi Zhurnal; Vol. 48 No. 6 (1996); 813-825 Український математичний журнал; Том 48 № 6 (1996); 813-825 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5281/7254 https://umj.imath.kiev.ua/index.php/umj/article/view/5281/7255 Copyright (c) 1996 Palyutkin V. G. |
| spellingShingle | Palyutkin, V. G. Палюткин, В. Г. Палюткин, В. Г. Distribution of eigenvalues of the Sturm-Liouville problem with slowly increasing potential |
| title | Distribution of eigenvalues of the Sturm-Liouville problem with slowly increasing potential |
| title_alt | Распределение собственных значений задачи Штурма - Лиувилля с медленно растущим потенциалом |
| title_full | Distribution of eigenvalues of the Sturm-Liouville problem with slowly increasing potential |
| title_fullStr | Distribution of eigenvalues of the Sturm-Liouville problem with slowly increasing potential |
| title_full_unstemmed | Distribution of eigenvalues of the Sturm-Liouville problem with slowly increasing potential |
| title_short | Distribution of eigenvalues of the Sturm-Liouville problem with slowly increasing potential |
| title_sort | distribution of eigenvalues of the sturm-liouville problem with slowly increasing potential |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5281 |
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