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arXiv · 1602.05228

On some a priori majorant of eigenvalues of Sturm--Liouville problems

A. A. Vladimirov
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Abstract

Let $M_\gamma$ be precise a priori majorant of first eigenvalues of Sturm--Liouville problems $-y"+qy=\lambda y,\quad y(0)=y(1)=0$, where $q\leqslant 0$ and $\int_0^1 |q|^\gamma\,dx=1$, $\gamma\in (0,1/2)$. It is shown that the inequality $M_\gamma<\pi^2$ is true.

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A. A. Vladimirov. 2016-02-04. On some a priori majorant of eigenvalues of Sturm--Liouville problems. https://arxiv.org/abs/1602.05228

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