6 papers
A Sharp Mass Threshold for Fractional Choquard Equations with Lower Hardy-Littlewood-Sobolev and \(L^2\)-Critical Terms
Yongpeng Chen, Zhipeng Yang
For \(\frac12\le s<1\), we study a fractional Choquard equation with prescribed mass and nonlinearities at the lower Hardy-Littlewood-Sobolev and \(L^2\)-critical exponents. The sh…
Normalized Solutions and Semiclassical Concentration for Upper-Critical Fractional Choquard Equations
Yergen Aikyn, Yongpeng Chen, Michael Ruzhansky +1
We study a fractional Choquard equation with an upper-critical Hartree term, an -supercritical Hartree perturbation, and a semiclassical potential under a prescribed -mas…
On the existence of normalized solutions to a class of fractional Choquard equation with potentials
Yongpeng Chen, Zhipeng Yang, Jianjun Zhang
This paper investigates the existence of normalized solutions to the nonlinear fractional Choquard equation: $$ (-Δ)^s u+V(x) u=λu+f(x)\left(I_α*\left(f|u|^q\right)\right)|u|^{q-2}…
On the existence of multiple normalized solutions for a class of fractional Choquard equations with mixed nonlinearities
Yongpeng Chen, Zhipeng Yang, Jianjun Zhang
We investigate the existence of normalized solutions for the following nonlinear fractional Choquard equation: $$ (-Δ)^s u+V(εx)u=λu+\left(I_α*|u|^q\right)|u|^{q-2} u+\left(I_α*|u|…
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|^…