Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stationary solutions of the Schr\"{o}dinger-Newton model - An ODE
  approach   We prove the existence and uniqueness of stationary spherically symmetric
positive solutions for the Schr\"{o}dinger-Newton model in any space dimension
$d$. Our result is based on an analysis of the corresponding system of second
order differential equations. It turns out that $d=6$ is critical for the
existence of finite energy solutions and the equations for positive spherically
symmetric solutions reduce to a Lane-Emden equation for all $d\geq 6$. Our
result implies in particular the existence of stationary solutions for
two-dimensional self-gravitating particles and closes the gap between the
variational proofs in $d=1$ and $d=3$.

1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th