Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: On the existence and blow-up of solutions for a mean field equation with
  variable intensities
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph