Year: 2024
Type: article
Abstract: This paper concerns the following planar Schrödinger–Poisson system \[ \begin{cases} -\Delta u + V(x) u + \phi u = |u|^{p-2} u &\textrm{in $\mathbb{R}^{2}$}, \\ \Delta \phi = u^{2}, \end{cases} \] where $p \geq 3$. By developing some new analytic techniques and variational methods, we establish a local compactness splitting lemma, and prove that this system possesses ground state solutions. We extend the case where $V(x)$ is a constant coefficient to the case where $V(x)$ is a variable coefficient. Some related results are improved.
Source: Taiwanese Journal of Mathematics
DOI: 10.11650/tjm/241004
Author: Ziqing Yuan
Institution: Shaoyang University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Award: G606261409
OpenAlex ID: W4403372071