Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Leighton's Comparison Theorem   We give a simple proof of a fairly flexible comparison theorem for equations
of the type $-(p(u'+su))'+rp(u'+su)+qu=0$ on a finite interval where $1/p$,
$r$, $s$, and $q$ are real and integrable. Flexibility is provided by two
functions which may be chosen freely (within limits) according to the situation
at hand. We illustrate this by presenting some examples and special cases which
include Schr\"odinger equations with distributional potentials as well as
Jacobi difference equations.

8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex