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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…
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…
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|^…
Bayesian Approach to Inverse Time-harmonic Acoustic Scattering from Sound-soft Obstacles with Phaseless Data
Zhipeng Yang, Xinping Gui, Ju Ming +1
This paper concerns the Bayesian approach to inverse acoustic scattering problems of inferring the position and shape of a sound-soft obstacle from phaseless far-field data generat…