Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Concentrating phenomenon for fractional nonlinear
  Schr\"{o}dinger-Poisson system with critical nonlinearity   In this paper, we study the following fractional Schr\"{o}dinger-Poisson
system \begin{equation*} \left\{
  \begin{array}{ll}
  \varepsilon^{2s}(-\Delta)^su+V(x)u+\phi u=g(u) & \hbox{in $\mathbb{R}^3$,}
  \varepsilon^{2t}(-\Delta)^t\phi=u^2,\,\, u>0& \hbox{in $\mathbb{R}^3$,}
  \end{array} \right. \end{equation*} where $s,t\in(0,1)$, $\varepsilon>0$ is a
small parameter. Under some suitable assumptions on potential function $V(x)$
and critical nonlinearity term $g(u)$, we construct a family of positive
solutions $u_{\varepsilon}\in H^s(\mathbb{R}^3)$ which concentrates around the
global minima of $V$ as $\varepsilon\rightarrow0$.

4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat