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math.AP2020
Positive solutions for the Schrödinger-Poisson system with steep potential well
Miao Du
In this paper, we consider the following Schrödinger-Poisson system \begin{equation*} \begin{cases} - Δu+λV(x)u+ μϕu=|u|^{p-2}u &\text{in },\cr -Δϕ=u^{2} &\text{in $\…
math.AP2017★ 5 cited
Ground states and high energy solutions of the planar Schrödinger-Poisson system
Miao Du, Tobias Weth
In this paper, we are concerned with the Schrödinger-Poisson system \begin{equation} (0.1)\qquad -Δu + u +ϕu = |u|^{p-2}u \quad \text{in}\ \mathbb{R}^{d},\qquad Δϕ= u^{2} \quad \te…