Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semi-linear cooperative elliptic systems involving Schr{\"o}dinger
  operators: Groundstate positivity or negativity   We study here the behavior of the solutions to a $2\times 2$ semi-linear
cooperative system involving Schr\" odinger operators (considered in its
variational form): $$LU:=(-\Delta + q(x))U = AU+\mu U + F(x,U) \quad{\rm in}\
\mathbb{R}^N$$ $$U(x)_{|x|\rightarrow \infty} \rightarrow 0$$ where $q$ is a
continuous positive potential tending to $+\infty$ at infinity; $\mu$ is a real
parameter varying near the principal eigenvalue of the system; $U$ is a column
vector with components $u_1$ and $u_2$ and $A$ is a square cooperative matrix
with constant coefficient. $F$ is a column vector with components $f_1$ and
$f_2$ depending eventually on $U$.

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The categories of this paper are: eess
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol