Geodesic
Majorants for eigenvalues of Sturm-Liouville problems with potentials lying in balls of weighted spaces
Sbornik. Mathematics, Tome 208 (2017) no. 9, pp. 1298-1311

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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: eigenvalue, Sobolev space.
Mots-clés : Sturm-Liouville problem 
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     author = {A. A. Vladimirov},
     title = {Majorants for eigenvalues of {Sturm-Liouville} problems with potentials lying in balls of weighted spaces},
     journal = {Sbornik. Mathematics},
     pages = {1298--1311},
     publisher = {mathdoc},
     volume = {208},
     number = {9},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_9_a2/}
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A. A. Vladimirov. Majorants for eigenvalues of Sturm-Liouville problems with potentials lying in balls of weighted spaces. Sbornik. Mathematics, Tome 208 (2017) no. 9, pp. 1298-1311. http://geodesic.mathdoc.fr/item/SM_2017_208_9_a2/