Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Brezis--Nirenberg problem for the H\'{e}non equation: ground state
  solutions   This work is devoted to the Dirichlet problem for the equation (-\Delta u =
\lambda u + |x|^\alpha |u|^{2^*-2} u) in the unit ball of $\mathbb{R}^N$.
  We assume that $\lambda$ is bigger than the first eigenvalues of the
laplacian, and we prove that there exists a solution provided $\alpha$ is small
enough. This solution has a variational characterization as a ground state.

22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas