Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ground state solutions for a semilinear elliptic problem with
  critical-subcritical growth   In this work, we study the of positive ground state solution for the
semilinear elliptic problem $$ \left\{ \begin{array} [c]{ll}% -\Delta
u=u^{p(x)-1},\quad u>0 & \mathrm{in}\,G\subseteq\mathbb{R}^{N}% ,\,N\geq3\\
u\in D_{0}^{1,2}(G), & \end{array} \right. $$ where $G$ is either
$\mathbb{R}^{N}$ or a bounded domain, and $p:G\rightarrow \mathbb{R}$ is a
continuous function assuming critical and subcritical values.

21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th