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
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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 $\gamma<1/3$.
Mots-clés : Sturm–Liouville problem
Keywords: estimate of eigenvalues. 
@article{INTO_2021_193_a3,
     author = {A. A. Vladimirov and E. S. Karulina},
     title = {On an a~priori majorant of the least eigenvalues of the {Sturm{\textendash}Liouville} problem},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {25--27},
     year = {2021},
     volume = {193},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_193_a3/}
}
TY  - JOUR
AU  - A. A. Vladimirov
AU  - E. S. Karulina
TI  - On an a priori majorant of the least eigenvalues of the Sturm–Liouville problem
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2021
SP  - 25
EP  - 27
VL  - 193
UR  - http://geodesic.mathdoc.fr/item/INTO_2021_193_a3/
LA  - ru
ID  - INTO_2021_193_a3
ER  - 
%0 Journal Article
%A A. A. Vladimirov
%A E. S. Karulina
%T On an a priori majorant of the least eigenvalues of the Sturm–Liouville problem
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2021
%P 25-27
%V 193
%U http://geodesic.mathdoc.fr/item/INTO_2021_193_a3/
%G ru
%F INTO_2021_193_a3
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/

[1] Ezhak S. S., “Otsenki pervogo sobstvennogo znacheniya zadachi Shturma—Liuvillya s usloviyami Dirikhle”, Kachestvennye svoistva reshenii differentsialnykh uravnenii i smezhnye voprosy spektralnogo analiza, YuNITI-DANA, M., 2012, 517–559

[2] Ezhak S. S., “Ob odnoi zadache minimizatsii funktsionala, porozhdennogo zadachei Shturma—Liuvillya s integralnym usloviem na potentsial”, Vestn. SamGU., 6 (128) (2015), 57–61

[3] Ezhak S. S., “On estimates for the first eigenvalue of the Sturm–Liouville problem with Dirichlet boundary conditions and integral condition”, Differential and Difference Equations with Applications, Springer-Verlag, New York, 2013, 387–394 | DOI | MR | Zbl

[4] Ezhak S., Telnova M., “On estimates for the first eigenvalue of some Sturm–Liouville problems with Dirichlet boundary conditions and a weighted integral condition”, Proc. Int. Workshop on the Qualitative Theory of Differential Equations “QUALITDE-2016”, A. Razmadze Math. Inst., Tbilisi, Georgia, 2016, 81–85 | MR