Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blow-up behavior of ground states for a nonlinear Schr\"{o}dinger system
  with attractive and repulsive interactions   We consider a nonlinear Schr\"odinger system arising in a two-component
Bose-Einstein condensate (BEC) with attractive intraspecies interactions and
repulsive interspecies interactions in $\mathbb{R}^2$. We get ground states of
this system by solving a constrained minimization problem. For some kinds of
trapping potentials, we prove that the minimization problem has a minimizer if
and only if the attractive interaction strength $a_i (i=1,2)$ of each component
of the BEC system is strictly less than a threshold $a^*$. %attractive
intraspecies interactions satisfies $a_i< %a^*= \|Q\|_2^2,\ i=1,\,2$, where $Q$
is the unique positive radial solution of $\Delta u-u+u^3=0$ in $\mathbb{R}^2$;
in contrast, there is no minimizer if either $a_i > a^*$ for $i=1$ or $2$, or
$a_1=a_2=a^*$. Furthermore, as $(a_1, a_2)\nearrow (a^*, a^*)$, the
asymptotical behavior for the minimizers of the minimization problem is
discussed. Our results show that each component of the BEC system concentrates
at a global minimum of the associated trapping potential.

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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
18
The categories of this paper are: econ