Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular limits for the bi-laplacian operator with exponential
  nonlinearity in $\R^4$   Let $\Omega$ be a bounded smooth domain in $\mathbb{R}^{4}$ such that for
some integer $d\geq1$ its $d$-th singular cohomology group with coefficients in
some field is not zero, then problem
  {\Delta^{2}u-\rho^{4}k(x)e^{u}=0 & \hbox{in}\Omega,
  u=\Delta u=0 & \hbox{on}\partial\Omega,
  has a solution blowing-up, as $\rho\to0$, at $m$ points of $\Omega$, for any
given number $m$.

7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ