Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A priori bounds and positive solutions for non-variational fractional
  elliptic systems   In this paper we study strongly coupled elliptic systems in non-variational
form involving fractional Laplace operators. We prove Liouville type theorems
and, by mean of the blow-up method, we establish a priori bounds of positive
solutions for subcritical and superlinear nonlinearities in a coupled sense. By
using those latter, we then derive the existence of positive solutions through
topological methods.

10
The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
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The categories of this paper are: stat
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
19
The categories of this paper are: eess
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The categories of this paper are: hep-ex
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: supr-con
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The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph