Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ground States for a nonlinear Schr\"odinger system with sublinear
  coupling terms   We study the existence of ground states for the coupled Schr\"odinger system
  \begin{equation} \left\{\begin{array}{lll} \displaystyle -\Delta
u_i+\lambda_i u_i= \mu_i |u_i|^{2q-2}u_i+\sum_{j\neq i}b_{ij}
|u_j|^q|u_i|^{q-2}u_i \\ u_i\in H^1(\mathbb{R}^n), \quad i=1,\ldots, d,
\end{array}\right. \end{equation} $n\geq 1$, for $\lambda_i,\mu_i >0$,
$b_{ij}=b_{ji}>0$ (the so-called "symmetric attractive case") and
$1<q<n/(n-2)^+$. We prove the existence of a nonnegative ground state
$(u_1^*,\ldots,u_d^*)$ with $u_i^*$ radially decreasing. Moreover we show that,
for $1<q<2$, such ground states are positive in all dimensions and for all
values of the parameters.

11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys