Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiclassical states of a linearly coupled critical fractional
  Schr\"{o}dinger system   This paper focuses on the linearly coupled critical fractional
Schr\"{o}dinger system \begin{equation*} \begin{cases}
\epsilon^{2s}(-\triangle)^s u +a(x)u=u^p+\lambda v\quad &\text{in}\
\mathbb{R}^N,\\ \epsilon^{2s}(-\triangle)^s v +b(x)v=v^{2_s^*-1}+\lambda u\quad
&\text{in}\ \mathbb{R}^N, \end{cases} \end{equation*} where $N>2s,$
$s\in(0,1),$ $p\in(1,2_s^*),$ $\epsilon$ and $\lambda$ are positive parameters,
$a,b\in C{(\mathbb{R}^N)}$ are positive potentials, and $(-\triangle)^s$ is the
fractional Laplacian operator. Under certain assumptions on $a$ and $\lambda,$
we obtain the existence, decay estimates and concentration property of positive
vector ground states for small $\epsilon.$ Furthermore, under an additional
assumption on potentials $a$ and $b$, we consider the multiplicity of positive
vector solutions for small $\epsilon$, which turn out to have similar decay
estimate and concentration property to those of the ground state for small
$\epsilon$.

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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph