Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniqueness and nondegeneracy of ground states for nonlinear
  Schr\"odinger equations with attractive inverse-power potential   We study uniqueness and nondegeneracy of ground states for stationary
nonlinear Schr\"odinger equations with a focusing power-type nonlinearity and
an attractive inverse-power potential. We refine the results of Shioji and
Watanabe (2016) and apply it to prove the uniqueness and nondegeneracy of
ground states for our equations. We also discuss the orbital instability of
ground state-standing waves.

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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ