Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitely many sign changing solutions of an elliptic problem involving
  critical Sobolev and Hardy-Sobolev exponent   We study the existence and multiplicity of sign changing solutions of the
following equation $ \begin{cases} -\Delta u = \mu
|u|^{2^{\star}-2}u+\frac{|u|^{2^{*}(t)-2}u}{|x|^t}+a(x)u \quad\text{in}\quad
\Omega, u=0 \quad\text{on}\quad\partial\Omega, \end{cases} $where $\Omega$ is a
bounded domain in $R^N$, $0\in\partial\Omega$, all the principal curvatures of
$\partial\Omega$ at $0$ are negative and $\mu\geq 0, \ \ a>0, \ \ N\geq 7, \ \
0<t<2, \ \ 2^{\star}=\frac{2N}{N-2}$ and $2^{\star}(t)=\frac{2(N-t)}{N-2}$.

35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: funct-an