Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dependence of Discrete Sturm-Liouville Eigenvalues on Problems   This paper is concerned with dependence of discrete Sturm-Liouville
eigenvalues on problems. Topologies and geometric structures on various spaces
of such problems are firstly introduced. Then, relationships between the
analytic and geometric multiplicities of an eigenvalue are discussed. It is
shown that all problems sufficiently close to a given problem have eigenvalues
near each eigenvalue of the given problem. So, all the simple eigenvalues live
in so-called continuous simple eigenvalue branches over the space of problems,
and all the eigenvalues live in continuous eigenvalue branches over the space
of self-adjoint problems. The analyticity, differentiability and monotonicity
of continuous eigenvalue branches are further studied.

1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ