Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of infinitely many solutions for a nonlocal elliptic PDE
  involving singularity   In this article, we will prove the existence of infinitely many positive weak
solutions to the following nonlocal elliptic PDE.
  \begin{align}
  (-\Delta)^s u&= \frac{\lambda}{u^{\gamma}}+ f(x,u)~\text{in}~\Omega,\nonumber
  u&=0~\text{in}~\mathbb{R}^N\setminus\Omega,\nonumber
  \end{align} where $\Omega$ is an open bounded domain in $\mathbb{R}^N$ with
Lipschitz boundary, $N>2s$, $s\in (0,1)$, $\gamma\in (0,1)$. We will employ
variational techniques to show the existence of infinitely many weak solutions
of the above problem.

10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph