Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Brezis-Nirenberg problem for a Kirchhoff type equation in high
  dimension   The present paper deals with a parametrized Kirchhoff type problem involving
a critical nonlinearity in high dimension. Existence, non existence and
multiplicity of solutions are obtained under the effect of a subcritical
perturbation by combining variational properties with a careful analysis of the
fiber maps of the energy functional associated to the problem. The particular
case of a pure power perturbation is also addressed. Through the study of the
Nehari manifolds we extend the general case to a wider range of the parameters.

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The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn