Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sign-changing blowing-up solutions for supercritical Bahri-Coron's
  problem   Let $\Omega$ be a bounded domain in $\R^n$, $n\ge 3$ with smooth boundary
$\partial\Omega$ and a small hole. We give the first example of sign-changing
{\it bubbling} solutions to the nonlinear elliptic problem $$
  -\Delta u=|u|^{{n+2\over n-2} +\ve -1 } u \, \, \mbox{ in } \Omega , \quad
\quad
  u=0 \mbox{ on } \partial \Omega, $$ where $\ve$ is a small positive
parameter. The basic cell in the construction is the sign-changing nodal
solution to the critical Yamabe problem $$ -\Delta w = |w|^{\frac{4}{n-2}} w, \
\ w \in {\mathcal D}^{1,2} (\R^n) $$ which has large number ($3n$) of kernels.

37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
3
The categories of this paper are: physics