Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak solutions of semilinear elliptic equations with Leray-Hardy
  potential and measure data   We study existence and stability of solutions of (E 1) --$\Delta$u + $\mu$
|x| 2 u + g(u) = $\nu$ in $\Omega$, u = 0 on $\partial$$\Omega$, where $\Omega$
is a bounded, smooth domain of R N , N $\ge$ 2, containing the origin, $\mu$
$\ge$ -- (N --2) 2 4 is a constant, g is a nondecreasing function satisfying
some integral growth assumption and $\nu$ is a Radon measure on $\Omega$. We
show that the situation differs according $\nu$ is diffuse or concentrated at
the origin. When g is a power we introduce a capacity framework to find
necessary and sufficient condition for solvability.

8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin