Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A fractional p-Laplacian problem with multiple critical Hardy-Sobolev
  nonlinearities   In this work, we study the existence of weak solution to the following quasi
linear elliptic problem involving the fractional $p$-Laplacian operator, a
Hardy potential and multiple critical Sobolev nonlinearities with
singularities, \begin{align*} (-\Delta_p)^su - \mu \dfrac{\vert u \vert^{p-2}
u}{\vert x \vert^{ps}} = \dfrac{\vert u\vert^{p^*_s(\beta)-2}u}{\vert x
\vert^{\beta}} + \dfrac{\vert u\vert^{p^*_s(\alpha )-2} u}{\vert x \vert^\alpha
}, \end{align*} where $ x \in \mathbb{R}^N$, $u\in D^{s,p}(\mathbb{R}^N)$,
$0<s<1$, $1<p<+\infty$, $N>sp$, $0<\alpha<sp$, $0<\beta<sp$, $\beta\neq\alpha$,
$\mu < \mu_H := \inf_{u \in D^{s,p}(\mathbb{R}^N) \backslash \{ 0 \}}
[u]_{s,p}^p / \vert\vert u \vert\vert_{s,p}^p > 0$. To prove the existence of
solution to the problem we have to formulate a refined version of the
concentration-compactness principle and, as an independent result, we have to
show that the extremals for the Sobolev inequality are attained.

17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph