Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positive solutions of semilinear elliptic problems with a Hardy
  potential   Let $\Omega \subset \mathbb{R}^N$ be a bounded domain and $\delta(x)$ be the
distance of a point $x\in \Omega$ to the boundary. We study the positive
solutions of the problem $\Delta u +\frac{\mu}{\delta(x)^2}u=u^p$ in $\Omega$,
where $p>0, \,p\ne 1$ and $\mu \in \mathbb{R},\,\mu\ne 0$ is smaller then the
Hardy constant. The interplay between the singular potential and the
nonlinearity leads to interesting structures of the solution sets. In this
paper we first give the complete picture of the radial solutions in balls. In
particular we establish for $p>1$ the existence of a unique large solution
behaving like $\delta^{- \frac2{p-1}}$ at the boundary. In general domains we
extend results of arXiv:arch-ive/1407.0288 and show that there exists a unique
singular solutions $u$ such that $u/\delta^{\beta_-}\to c$ on the boundary for
an arbitrary positive function $c \in C^{2+\gamma}(\partial\Omega) \, (\gamma
\in (0,1)), c \ge 0$. Here $\beta_-$ is the smaller root of
$\beta(\beta-1)+\mu=0$.

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The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat