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math.AP2020★ 5 cited
Existence and concentration of solution for Schrödinger-Poisson system with local potential
Zhipeng Yang, Yuanyang Yu
In this paper, we study the following nonlinear Schrödinger-Poisson type equation \begin{equation*} \begin{cases} -\varepsilon^2Δu+V(x)u+K(x)ϕu=f(u)&\text{in}\ \mathbb{R}^3,\\ -\va…
math.AP2020
Multiplicity of solutions for a class of critical Schrödinger-Poisson system with two parameters
Yongpeng Chen, Zhipeng Yang
We study a class of critical Schrödinger-Poisson system of the form \begin{equation*} \begin{cases} -Δu+λV(x)u+ϕu=μ|u|^{p-2}u+|u|^{4}u& \quad x\in \mathbb{R}^3,\\ -Δϕ=u^2&\quad x\i…
math.AP2020
Concentration of positive ground state solutions for critical Kirchhoff equation with competing potentials
Yongpeng Chen, Zhipeng Yang
In this paper, we consider the following singularly perturbed Kirchhoff equation \begin{equation*} -(\varepsilon^2a+\varepsilon b\int_{\mathbb{R}^3}|\nabla u|^2dx)Δu+V(x)u=P(x)|u|^…