Geodesic
On an a~priori majorant of the least eigenvalues of the Sturm--Liouville problem
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 193 (2021), pp. 25-27.

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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 $\gamma1/3$.
Mots-clés : Sturm–Liouville problem
Keywords: estimate of eigenvalues. 
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A. A. Vladimirov; E. S. Karulina. On an a~priori majorant of the least eigenvalues of the Sturm--Liouville problem. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 193 (2021), pp. 25-27. http://geodesic.mathdoc.fr/item/INTO_2021_193_a3/

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