Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some a priori majorant of eigenvalues of Sturm--Liouville problems   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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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an