Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of multiple solutions to an elliptic problem with measure data   In this paper we prove the existence of multiple nontrivial solutions of the
following equation. \begin{align*} \begin{split} -\Delta_{p}u & = \lambda
|u|^{q-2}u+f(x,u)+\mu\,\,\mbox{in}\,\,\Omega, u & = 0\,\, \mbox{on}\,\,
\partial\Omega; \end{split} \end{align*} where $\Omega \subset \mathbb{R}^N$ is
a smooth bounded domain with $N \geq 3$, $1 < q^{\prime} < q < p-1; \;
\lambda,\;$ and $f$ satisfies certain conditions, $\mu>0$ is a Radon measure,
$q^{\prime}=\frac{q}{q-1}$ is the conjugate of $q$.

17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph