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.

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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. 
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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/

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