Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ground States of Two-Component Attractive Bose-Einstein Condensates I:
  Existence and Uniqueness   We study ground states of two-component Bose-Einstein condensates (BEC) with
trapping potentials in $R^2$, where the intraspecies interaction $(-a_1,-a_2)$
and the interspecies interaction $-\beta$ are both attractive, $i.e,$ $a_1$,
$a_2$ and $\beta $ are all positive. The existence and non-existence of ground
states are classified completely by investigating equivalently the associated
$L^2$-critical constraint variational problem. The uniqueness and
symmetry-breaking of ground states are also analyzed under different types of
trapping potentials as $\beta \nearrow \beta ^*=a^*+\sqrt{(a^*-a_1)(a^*-a_2)}$,
where $0<a_i<a^*:=\|w\|^2_2$ ($i=1,2$) is fixed and $w$ is the unique positive
solution of $\Delta w-w+w^3=0$ in $R^2$. The semi-trivial limit behavior of
ground states is tackled in the companion paper [12].

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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: cs