Geodesic
On the first eigenvalue of the Sturm--Liouville problem with a weighted integral condition on the potential
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. 87-98

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider the Sturm–Liouville problem on the segment $[0,1]$ with the Dirichlet boundary conditions and a weighted integral condition on the potential, which allows the potential to have different orders of singularities at the endpoints of the segment $[0,1]$. We obtain an additional integral condition for the potential under which the first eigenvalue of the problem exists. For values of the parameters of the weighted integral condition that provide the existence of potentials satisfying both integral conditions, we examine estimates of the first eigenvalue of the problem.
Mots-clés : Sturm–Liouville problem
Keywords: extremal estimate, first eigenvalue, variational principle, minimization of a functional, spectral problem, boundary-value problem, Dirichlet conditions, weighted integral condition. 
@article{INTO_2021_193_a8,
     author = {S. S. Ezhak and M. Yu. Telnova},
     title = {On the first eigenvalue of the {Sturm--Liouville} problem with a weighted integral condition on the potential},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {87--98},
     publisher = {mathdoc},
     volume = {193},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_193_a8/}
}
TY  - JOUR
AU  - S. S. Ezhak
AU  - M. Yu. Telnova
TI  - On the first eigenvalue of the Sturm--Liouville problem with a weighted integral condition on the potential
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2021
SP  - 87
EP  - 98
VL  - 193
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2021_193_a8/
LA  - ru
ID  - INTO_2021_193_a8
ER  - 
%0 Journal Article
%A S. S. Ezhak
%A M. Yu. Telnova
%T On the first eigenvalue of the Sturm--Liouville problem with a weighted integral condition on the potential
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2021
%P 87-98
%V 193
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2021_193_a8/
%G ru
%F INTO_2021_193_a8
S. S. Ezhak; M. Yu. Telnova. On the first eigenvalue of the Sturm--Liouville problem with a weighted integral condition on the potential. 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. 87-98. http://geodesic.mathdoc.fr/item/INTO_2021_193_a8/