Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the oscillation properties of eigenfunctions of Sturm--Liouville
  problem with singular coefficients   In the paper we consider singular spectral Sturm--Liouville problem
$-(py')'+(q-\lambda r)y=0$, $(U-1)y^{\vee}+i(U+1)y^{\wedge}=0$, where function
$p\in L_{\infty}[0,1]$ is uniformly positive, generalized functions $q,r\in
W_2^{-1}[0,1]$ are real-valued and unitary matrix $U\in\mathbb C^{2\times 2}$
is diagonal. The main goal is to prove that well-known (for smooth case) facts
about number and distribution of zeros of eigenfunctions hold in general case.

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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph