Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ground state for the Schr\"odinger operater with the weighted Hardy
  potential   We establish the existence of ground states on Euclidean space for the
Laplace operator involving the Hardy type potential. This gives rise to the
existence of the principal eigenfunctions for the Laplace operator involving
weighted Hardy potentials.
  We also obtain a higher integrability property for the principal
eigenfunction. This is used to examine the behaviour of the principal
eigenfunction around 0.

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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex