English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we study the following nonlinear Schr\"odinger-Poisson typeequation \begin{equation*} \begin{cases} -\varepsilon^2\Delta u+V(x)u+K(x)\phiu=f(u)&\text{in}\ \mathbb{R}^3,\\ -\varepsilon^2\Delta \phi=K(x)u^2&\text{in}\\mathbb{R}^3, \end{cases} \end{equation*} where $\varepsilon>0$ is a smallparameter, $V: \mathbb{R}^3\rightarrow \mathbb{R}$ is a continuous potentialand $K: \mathbb{R}^3\rightarrow \mathbb{R}$ is used to describe the electroncharge. Under suitable assumptions on $V(x), K(x)$ and $f$, we prove existenceand concentration properties of ground state solutions for $\varepsilon>0$small. Moreover, we summarize some open problems for the Schr\"odinger-Poissonsystem.

Existence and concentration of solution for Schr\"odinger-Poisson system with local potential