Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and concentration of positive bound states for the
  Schr\"odinger-Poisson system with potentials   In this article we study the existence and concentration behavior of bound
states for a nonlinear Schr\"odinger-Poisson system with a parameter
$\varepsilon>0$. Under some suitable conditions on the potential functions, we
prove that for $\varepsilon$ small the system has a positive solution that
concentrates at a point which is a global minimum of the minimax function
associated to the related autonomous problem.

24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph