Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of stable solutions of a Lane-Emden type system   We examine the system given by \hfill -\Delta u = \lambda (v+1)^p \qquad
\Omega \hfill -\Delta v = \gamma (u+1)^\theta \qquad \Omega, \hfill u = v =0
\qquad \quad \partial \Omega, where $ \lambda,\gamma$ are positive parameters
and where $ 1 < p \le \theta$ and where $ \Omega$ is a smooth bounded domain in
$ R^N$. We show the extremal solutions associated with the above system are
bounded provided
  [\frac{N}{2} < 1 + \frac{2(\theta+1)}{p\theta -1} (\sqrt{\frac{p \theta
(p+1)}{\theta +1}} + \sqrt{\frac{p \theta (p+1)}{\theta +1} - \sqrt{\frac{p
\theta (p+1)}{\theta +1}}})]

5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph