Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of nonnegative solutions to static
  Schr\"{o}dinger-Hartree and Schr\"{o}dinger-Maxwell equations with combined
  nonlinearities   In this paper, we are concerned with static Schr\"{o}dinger-Hartree and
Schr\"{o}dinger-Maxwell equations with combined nonlinearities. We derive the
explicit forms for positive solution $u$ in the critical case and non-existence
of nontrivial nonnegative solutions in the subcritical cases (see Theorem
\ref{Thm0} and \ref{Thm1}). The arguments used in our proof is a variant (for
nonlocal nonlinearity) of the direct moving spheres method for fractional
Laplacians in \cite{CLZ}. The main ingredients are the variants (for nonlocal
nonlinearity) of the maximum principles, i.e., \emph{Narrow region principle}
(Theorem \ref{Thm2} and \ref{Thm3}).

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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph