Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behaviour of the positive spectrum for a family of periodic
  Sturm-Liouville problems in the transition from a definite problem to
  indefinite one   Spectral problem for a family of periodic Sturm--Liouville problems \[
u''+\lambda^2(a(x)-a)u=0 \] depending on the parameter (a\in\mathbb R) is
considered. An interpolation formula describing the behaviour of the branches
of the spectrum in the transition from a definite problem to indefinite one is
obtained.

27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con