Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ground state solutions for the nonlinear fractional Schrodinger-Poisson
  system   In this paper, we study the existence of ground state solutions for the
nonlinear fractional Schr\"{o}dinger-Poisson system \begin{equation*} \left\{
\begin{array}{ll} (-\Delta)^su+V(x)u+\phi u=|u|^{p-1}u, & \hbox{in
$\mathbb{R}^3$,} (-\Delta)^s\phi=u^2,& \hbox{in $\mathbb{R}^3$,} \end{array}
\right. \end{equation*} where $2<p<2_s^{\ast}-1 = \frac{3+2s}{3-2s}$,
$s\in(\frac{3}{4},1)$. Under certain assumptions on $V$, a nontrivial ground
state solution $(u,\phi)$ is established through using a monotonicity trick and
global compactness Lemma. As its supplementary results, we prove some
nonexistence results in the case of $1<p\leq 2$ and $p=2_s^{\ast}-1$.

19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th