Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonexistence results for a class of nonlinear elliptic equations
  involving critical Sobolev exponents   In this paper we study the problem of bifurcation from the origin of
solutions of elliptic Dirichlet problems involving critical Sobolev exponent,
defined on a bounded domain $\Omega$ in $\mathbb{R} ^N$: we prove that the
first critical case are $N=3, 4$ (not only N=3, as just proved by Brezis and
Nirenberg), exhibiting two nonexistence results for a class of elliptic problem
in these dimensions.

26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th