Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Liouvillian solutions for second order linear differential equations
  with polynomial coefficients   In this paper we present an algebraic study concerning the general second
order linear differential equation with polynomial coefficients. By means of
Kovacic's algorithm and asymptotic iteration method we find a degree
independent algebraic description of the spectral set: the subset, in the
parameter space, of Liouiville integrable differential equations. For each
fixed degree, we prove that the spectral set is a countable union of non
accumulating algebraic varieties. This algebraic description of the spectral
set allow us to bound the number of eigenvalues for algebraically
quasi-solvable potentials in the Schr\"odinger equation.

16
The categories of this paper are: stat
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg