Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Liouville Theorem for the Higher Order Fractional Laplacian   We deal with the higher-order fractional Laplacians by two methods: the
integral method and the system method. The former depends on the integral
equation equivalent to the differential equation.
  The latter works directly on the differential equations. We first derive
nonexistence of positive solutions, often known as the Liouville type theorem,
for the integral and differential equations. Then through an delicate
iteration, we show symmetry for positive solutions.

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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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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: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat