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Yongpeng Chen

Publications and source records attributed to Yongpeng Chen.

6 recordsLinked to original sources
arXiv2026

A Sharp Mass Threshold for Fractional Choquard Equations with Lower Hardy-Littlewood-Sobolev and \(L^2\)-Critical Terms

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 sharp Hardy-Littlewood-Sobolev and Choquard Gagliardo-Nirenberg inequalities determine an explicit critical mass \(a_*\). For \(0 a_*\), the energy is unbounded from below on the mass sphere, while the Pohozaev set is nonempty.

math.AP↗
arXiv2026

Normalized Solutions and Semiclassical Concentration for Upper-Critical Fractional Choquard Equations

We study a fractional Choquard equation with an upper-critical Hartree term, an $L^2$-supercritical Hartree perturbation, and a semiclassical potential under a prescribed $L^2$-mass constraint. The potential is bounded and nonnegative, has a nonempty zero set, and has a positive lower limit at infinity. For every prescribed mass and all sufficiently small semiclassical parameters, we prove the existence of a pair of normalized solutions $\pm u_\varepsilon$ with a negative Lagrange multiplier. The proof combines a strict energy bound below the critical one-bubble level, compactness modulo translations for the autonomous ground-state set, a simultaneous cutoff of both Hartree terms, and a localized constrained mountain-pass argument. Moreover, suitable translates of $u_\varepsilon$ converge strongly in $H^s(\mathbb{R}^N)$ to a positive autonomous ground state, and the corresponding concentration points approach the zero set of the potential as $\varepsilon\to0$.

math.AP↗
arXiv2026

On the existence of normalized solutions to a class of fractional Choquard equation with potentials

This paper investigates the existence of normalized solutions to the nonlinear fractional Choquard equation: $$ (-Δ)^s u+V(x) u=λu+f(x)\left(I_α*\left(f|u|^q\right)\right)|u|^{q-2} u+g(x)\left(I_α*\left(g|u|^p\right)\right)|u|^{p-2} u, \quad x \in \mathbb{R}^N $$ subject to the mass constraint $$ \int_{\mathbb{R}^N}|u|^2 d x=a>0, $$ where $N>2 s, s \in(0,1), α\in(0, N)$, and $\frac{N+α}{N} \leq q<p \leq \frac{N+α+2 s}{N}$. Here, the parameter $λ\in \mathbb{R}$ appears as an unknown Lagrange multiplier associated with the normalization condition. By employing variational methods under appropriate assumptions on the potentials $V(x), f(x)$, and $g(x)$, we establish several existence results for normalized solutions.

math.AP↗
arXiv2024

On the existence of multiple normalized solutions for a class of fractional Choquard equations with mixed nonlinearities

We investigate the existence of normalized solutions for the following nonlinear fractional Choquard equation: $$ (-Δ)^s u+V(εx)u=λu+\left(I_α*|u|^q\right)|u|^{q-2} u+\left(I_α*|u|^p\right)|u|^{p-2} u, \quad x \in \mathbb{R}^N, $$ subject to the constraint $$ \int_{\mathbb{R}^N}|u|^2 \mathrm{d}x=a>0, $$ where $N>2 s, s \in(0,1), α\in(0, N), \frac{N+α}{N} 0$ is a parameter, and $λ\in \mathbb{R}$ serves as an unknown parameter acting as a Lagrange multiplier. By employing the Lusternik-Schnirelmann category theory, we estimate the number of normalized solutions to this problem by virtue of the category of the set of minimum points of the potential function $V$.

math.AP↗
arXiv2020

Concentration of positive ground state solutions for critical Kirchhoff equation with competing potentials

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|^{p-2}u+Q(x)|u|^4u,\quad x\in\mathbb{R}^3, \end{equation*} where $\varepsilon>0$ is a small parameter, $a, b > 0$ are constants, $p\in(4,6)$ and $V, P, Q$ are potential functions satisfying some competing conditions. We prove the existence of a positive ground state solution by using variational methods, and we determine a concrete set related to the potentials $V,P$ and $Q$ as the concentration position of these ground state solutions as $\varepsilon\to0$.

math.AP↗
arXiv2020

Multiplicity of solutions for a class of critical Schrödinger-Poisson system with two parameters

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\in \mathbb{R}^3,\\ \end{cases} \end{equation*} where $λ, μ>0$ are two parameters, $p\in(4,6)$ and $V$ satisfies some potential well conditions. By using the variational arguments, we prove the existence of positive ground state solutions for $λ$ large enough and $μ>0$, and their asymptotical behavior as $λ\to\infty$. Moreover, by using Ljusternik-Schnirelmann theory, we obtain the existence of multiple positive solutions if $λ$ is large and $μ$ is small.

math.AP↗