Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasilinear elliptic equations with sub-natural growth terms in bounded
  domains   We consider the existence of positive solutions to weighted quasilinear
elliptic differential equations of the type \[ \begin{cases} - \Delta_{p, w} u
= \sigma u^{q} & \text{in $\Omega$}, \\ u = 0 & \text{on $\partial \Omega$}
\end{cases} \] in the sub-natural growth case $0 < q < p - 1$, where $\Omega$
is a bounded domain in $\mathbb{R}^{n}$, $\Delta_{p, w}$ is a weighted
$p$-Laplacian, and $\sigma$ is a nonnegative (locally finite) Radon measure on
$\Omega$. We give criteria for the existence problem. For the proof, we
investigate various properties of $p$-superharmonic functions, especially the
solvability of Dirichlet problems with infinite measure data.

20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs