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Mat. Sb., 2017, Volume 208, Number 9, Pages 42–55 (Mi msb8741)  

Majorants for eigenvalues of Sturm-Liouville problems with potentials lying in balls of weighted spaces

A. A. Vladimirov

Federal Research Center "Computer Science and Control" of Russian Academy of Sciences

Abstract: We study the problem concerning an exact a priori majorant for the least eigenvalue of the Sturm-Liouville problem
$$ -y"+qy=\lambda y,\qquad y(0)=y(1)=0 $$
with a condition of the form $\displaystyle\int_0^1 rq^\gamma dx\leqslant 1$ on the potential, where the weight $r\in C(0,1)$ is uniformly positive on the interval $(0,1)$. We give a constructive proof that this majorant is attainable for all $\gamma>1$ and, for a certain natural extension of the class of admissible potentials, also for $\gamma=1$.
Bibliography: 9 titles.

Keywords: Sturm-Liouville problem, eigenvalue, Sobolev space.

Funding Agency Grant Number
Russian Science Foundation 17-11-01215
This research was supported by the Russian Science Foundation (grant no. 17-11-01215).


DOI: https://doi.org/10.4213/sm8741

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English version:
Sbornik: Mathematics, 2017, 208:9, 1298–1311

Bibliographic databases:

UDC: 517.927+517.984
MSC: 34L15
Received: 20.05.2016 and 04.04.2017

Citation: A. A. Vladimirov, “Majorants for eigenvalues of Sturm-Liouville problems with potentials lying in balls of weighted spaces”, Mat. Sb., 208:9 (2017), 42–55; Sb. Math., 208:9 (2017), 1298–1311

Citation in format AMSBIB
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