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math.AP2024
Ground states of planar Schrödinger-Poisson systems with an unbounded potential
Miao Du, Jiaxin Xu
In this paper, we deal with a class of planar Schrödinger-Poisson systems, namely, $-Δu+V(x)u+\fracγ{2π}\bigl(\log(|\cdot|)\ast|u|^{2}\bigr)u=b|u|^{p-2}u\ \text{in}\ \mathbb{R}^{2}…
math.AP2023
On a class of planar Schrödinger-Poisson system with a bounded potential well
Miao Du, Jiaxin Xu
In this paper, we deal with the planar Schrödinger-Poisson system \begin{equation*}\begin{cases} -Δu + V(x) u + ϕu = b|u|^{p-2} u \ &\text{in}\ \mathbb{R}^{2},\\Δϕ= u^{2} &\text{in…