|
This article is cited in 1 scientific paper (total in 1 paper)
On an a priori majorant of the least eigenvalues of the Sturm–Liouville problem
A. A. Vladimirovab, E. S. Karulinac a Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
b Federal Research Center ‘Informatics and Control’ of Russian Academy of Science
c Plekhanov Russian State University of Economics, Moscow
Abstract:
We examine the exact a priori majorant $M_\gamma\rightleftharpoons\sup\limits_{q\in A_\gamma}\lambda_0(q)$ of the least eigenvalue of the Sturm–Liouville problem
$-y''+qy=\lambda y$, $y(0)=y(1)=0$, with a potential $q\in C[0,1]$ of the class $A_\gamma$ determined by the conditions $q\le 0$ and $\int\limits_0^1|q|^\gamma dx=1$, where $\gamma\in(0,1/2)$. For this majorant, we prove the strict estimate $M_\gamma<\pi^2$. The last estimate was known earlier in the case where $\gamma<1/3$.
Keywords:
Sturm–Liouville problem, estimate of eigenvalues.
Citation:
A. A. Vladimirov, E. S. Karulina, “On an a priori majorant of the least eigenvalues of the Sturm–Liouville problem”, Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 193, VINITI, Moscow, 2021, 25–27
Linking options:
https://www.mathnet.ru/eng/into797 https://www.mathnet.ru/eng/into/v193/p25
|
Statistics & downloads: |
Abstract page: | 132 | Full-text PDF : | 52 | References: | 12 |
|