Affiliation:
1. School of Mathematics and Statistics, Guizhou University, Guiyang, China
2. School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, China
Abstract
In this paper, we are concerned with the following Schrödinger-Poisson system
$$
\begin{cases}
-\Delta u+u+\lambda\phi u= Q(x)|u|^{4}u+\mu
\dfrac{|x|^\beta}{1+|x|^\beta}|u|^{q-2}u&in \mathbb{R}^3,
-\Delta \phi=u^{2} &in \mathbb{R}^3,
\end{cases}
$$
where $0< \beta<3$, $6<q<6+2\beta$, $Q(x)$ is a positive continuous function on $\mathbb{R}^3$, $\lambda,\mu>0$ are real parameters. By the variational method and the Nehari method, we obtain that the system has $k$ positive solutions.
Bibliography: 31 titles.
Funder
National Natural Science Foundation of China
Publisher
Steklov Mathematical Institute