Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On bifurcation for semilinear elliptic Dirichlet problems on shrinking
  domains   We consider the Dirichlet problem for semilinear elliptic equations on a
bounded domain which is diffeomorphic to a ball and investigate bifurcation
from a given (trivial) branch of solutions, where the radius of the ball serves
as bifurcation parameter. Our methods are based on well known results from
variational bifurcation theory, which we outline in a separate section for the
readers' convenience.

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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph