Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Choquard logarithmic equation involving fractional Laplacian
  operator and a nonlinearity with exponential critical growth   In the present work we investigate the existence and multiplicity of
nontrivial solutions for the Choquard Logarithmic equation
$(-\Delta)^{\frac{1}{2}} u + au + \lambda (\ln|\cdot|\ast |u|^{2})u = f(u)
\textrm{ in } \mathbb{R}$, for $ a>0 $, $ \lambda >0 $ and a nonlinearity $f$
with exponential critical growth. We prove the existence of a nontrivial
solution at the mountain pass level and a nontrivial ground state solution
under exponential critical and subcritical growth. Morever, when $ f $ has
subcritical growth we guarantee the existence of infinitely many solutions, via
genus theory.

10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an