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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| Datum: | 1996 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1996
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| Online Zugang: | 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| Zusammenfassung: | 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 \([x_ - (R), x_ + (R)],R \in \Re \) . |
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