Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On solvability of a class of nonlinear elliptic type equation with
  variable exponent   In this paper, we study the Dirichlet problem for the implicit degen- erate
nonlinear elliptic equation with variable exponent in a bounded domain. We
obtain sufficient conditions for the existence of a solution with- out
regularization and any restriction between the exponents. Furthermore, we
define the domain of the operator generated by posed problem and investigate
its some properties and also its relations with known spaces that enable us to
prove existence theorem.

28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph