Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple solutions for a self-consistent Dirac equation in two
  dimensions   This paper is devoted to the variational study of an effective model for the
electron transport in a graphene sample. We prove the existence of infinitely
many stationary solutions for a nonlin-ear Dirac equation which appears in the
WKB limit for the Schr{\"o}dinger equation describing the semi-classical
electron dynamics. The interaction term is given by a mean field,
self-consistent potential which is the trace of the 3D Coulomb potential.
Despite the nonlinearity being 4-homogeneous, compactness issues related to the
limiting Sobolev embedding $H^{\frac{1}{2}}(\Omega,\mathbb{C})\rightarrow L^{4}
(\Omega,\mathbb{C})$ are avoided thanks to the regular-ization property of the
operator $(-\Delta)^{-\frac{1}{2}$. This also allows us to prove smoothness of
the solutions. Our proof follows by direct arguments.

0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs