Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on a multiplicity result for the mean field equation on compact
  surfaces   We are concerned with a Liouville-type equation with exponential
nonlinearities on a compact surface which describes the mean field equation of
the equilibrium turbulence with arbitrarily signed vortices. We provide the
first multiplicity result for this class of equations by using Morse theory.

9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph