Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rabinowitz alternative for non-cooperative elliptic systems on geodesic
  balls   The purpose of this paper is to study properties of continua (closed
connected sets) of nontrivial solutions of non-cooperative elliptic systems
considered on geodesic balls in $S^n$. In particular, we have shown that if the
geodesic ball is a hemisphere, then these continua are unbounded. It is also
shown that the phenomenon of global symmetry-breaking bifurcation of such
solutions occurs. Since the problem is variational and SO(n)-symmetric, we
apply the techniques of equivariant bifurcation theory to prove the main
results of this article. As the topological tool we use the degree theory for
SO(n)-invariant strongly indefinite functionals defined in A.
Go{\l}\c{e}biewska, S. Rybicki, \emph{Global bifurcations of critical orbits of
$G$-invariant strongly indefinite functionals}, Nonl. Anal. {74} (2011),
1823-1834..

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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: stat
10
The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
1
The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph