Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical gauged Schr\"{o}dinger equations in R^2 with vanishing
  potentials   We study a class of gauged nonlinear Schr\"{o}dinger equations in the plane.
We obtain existence of two nontrivial solutions via the Mountain-Pass theorem
and Ekeland's variational principle. Moreover, we prove existence of infinitely
many solutions for odd nonlinearities.

9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph