46 citations · 137 across the 27 of their papers we have counts for
27 papers
Quantitative stability of a nonlocal Sobolev inequality
Paolo Piccione, Minbo Yang, Shuneng Zhao
In this paper, we study the quantitative stability of the nonlocal Soblev inequality \begin{equation*} S_{HL}\left(\int_{\mathbb{R}^N}\big(|x|^{-μ} \ast |u|^{2_μ^{\ast}}\big)|u|^{2…
Remainder terms of a nonlocal Sobolev inequality1
Shengbing Deng, Xingliang Tian, Minbo Yang +1
In this note we study a nonlocal version of the Sobolev inequality \begin{equation*} \int_{\mathbb{R}^N}|\nabla u|^2 dx \geq S_{HLS}\left(\int_{\mathbb{R}^N}\big(|x|^{-α} \ast u^{2…
Stein-Weiss type inequality on the upper half space and its applications
Xiang Li, Zifei Shen, Marco Squassina +1
In this paper, we establish some Stein-Weiss type inequalities with general kernels on the upper half space and study the existence of extremal functions for this inequality with t…
On a critical Maxwell equation in nonlocal media
Minbo Yang, Weiwei Ye, Shuijin Zhang
In this paper, we study the existence of solutions for a critical time-harmonic Maxwell equation in nonlocal media. By introducing some suitable Coulomb spaces involving curl opera…
Construction of infinitely many solutions for a critical Choquard equation via local Pohožaev identities
Fashun Gao, Vitaly Moroz, Minbo Yang +1
In this paper, we study a class of the critical Choquard equations with axisymmetric potentials, $$ -Δu+ V(|x'|,x'')u =\Big(|x|^{-4}\ast |u|^{2}\Big)u\hspace{4.14mm}\mbox{in}\hspac…
Local Uniqueness of blow-up solutions for critical Hartree equations in bounded domain
Marco Squassina, Minbo Yang, Shunneng Zhao
In this paper we are interested in the following critical Hartree equation \begin{equation*} \begin{cases} -Δu =\displaystyle{\Big(\int_Ω\frac{u^{2_μ^\ast} (ξ)}{|x-ξ|^μ}dξ\Big)u^{2…
Localized semiclassical states for Hamiltonian elliptic systems in dimension two
Hui Zhang, Minbo Yang, Jianjun Zhang +1
In this paper, we consider the Hamiltonian elliptic system in dimension two\begin{equation}\label{1.5}\aligned \left\{ \begin{array}{lll} -ε^2Δu+V(x)u=g(v)\ & \text{in}\quad \mathb…
Critical gauged Schrödinger equations in R^2 with vanishing potentials
Liejun Shen, Marco Squassina, Minbo Yang
We study a class of gauged nonlinear Schrödinger equations in the plane. We obtain existence of two nontrivial solutions via the Mountain-Pass theorem and Ekeland's variational pri…
High energy positive solutions for a coupled Hartree system with Hardy-Littlewood-Sobolev critical exponents
Fashun Gao, Haidong Liu, Vitaly Moroz +1
We study the coupled Hartree system $$ \left\{\begin{array}{ll} -Δu+ V_1(x)u =α_1\big(|x|^{-4}\ast u^{2}\big)u+β\big(|x|^{-4}\ast v^{2}\big)u &\mbox{in}\ \mathbb{R}^N,\\[1mm] -Δv+…
Nondegeneracy of solutions for a critical Hartree equation
Jacques Giacomoni, Yuanhong Wei, Minbo Yang
The aim of this paper is to prove the nondegeneracy of the unique positive solutions for the following critical Hartree type equations when is close to , $$ -Δu=\left(I_μ\…
Uniqueness and nondegeneracy of solutions for a critical nonlocal equation
Lele Du, Minbo Yang
The aim of this paper is to classify the positive solutions of the nonlocal critical equation: …
On elliptic equations with Stein-Weiss type convolution parts
Lele Du, Fashun Gao, Minbo Yang
The aim of this paper is to study the critical elliptic equations with Stein-Weiss type convolution parts $$ \displaystyle-Δu =\frac{1}{|x|^α}\left(\int_{\mathbb{R}^{N}}\frac{|u(y)…
Existence of solutions for critical Choquard equations via the concentration compactness method
Fashun Gao, Edcarlos D. da Silva, Minbo Yang +1
In this paper we consider the nonlinear Choquard equation $$ -Δu+V(x)u =\left(\int_{\mathbb{R}^N}\frac{G(y,u)}{|x-y|^μ}dy\right)g(x,u)\hspace{4.14mm}\mbox{in}\hspace{1.14mm} \mathb…
Semiclassical states for Choquard type equations with critical growth: critical frequency case
Yanheng Ding, Fashun Gao, Minbo Yang
In this paper we are interested in the existence of semiclassical states for the Choquard type equation $$ -\vr^2Δu +V(x)u =\Big(\int_{\R^N} \frac{G(u(y))}{|x-y|^μ}dy\Big)g(u) \qua…
On the critical Choquard equation with potential well
Fashun Gao, Zifei Shen, Minbo Yang
In this paper we are interested in the following nonlinear Choquard equation $$ -Δu+(λV(x)-β)u =\big(|x|^{-μ}\ast |u|^{2_μ^{\ast}}\big)|u|^{2_μ^{\ast}-2}u\hspace{4.14mm}\mbox{in}\h…
A strongly indefinite Choquard equation with critical exponent due to the Hardy-Littlewood-Sobolev inequality
Fashun Gao, Minbo Yang
In this paper we are concerned with the following nonlinear Choquard equation $$-Δu+V(x)u =\left(\int_{\mathbb{R}^N}\frac{G(y,u)}{|x-y|^μ}dy\right)g(x,u)\hspace{4.14mm}\mbox{in}\hs…
Singularly perturbed critical Choquard equations
Claudianor O. Alves, Fashun Gao, Marco Squassina +1
In this paper we study the semiclassical limit for the singularly perturbed Choquard equation $$ -\vr^2Δu +V(x)u =\vr^{μ-3}\Big(\int_{\R^3} \frac{Q(y)G(u(y))}{|x-y|^μ}dy\Big)Q(x)g(…
On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents
Fashun Gao, Minbo Yang
We consider the following nonlinear Choquard equation with Dirichlet boundary condition $$-Δu =\left(\int_Ω\frac{|u|^{2_μ^{\ast}}}{|x-y|^μ}dy\right)|u|^{2_μ^{\ast}-2}u+λf(u)\hspace…
Stability and instability of standing waves for a generalized Choquard equation with potential
Zhipeng Cheng, Minbo Yang
We are going to study the standing waves for a generalized Choquard equation with potential: $$ -i\partial_t u-Δu+V(x)u=(|x|^{-μ}\ast|u|^p)|u|^{p-2}u, \ \ \hbox{in}\ \ \mathbb{R}\t…
Multi-peak solutions for nonlinear Choquard equation with a general nonlinearity
Minbo Yang, Jianjun Zhang, Yimin Zhang
In this paper, we study a class of nonlinear Choquard type equations involving a general nonlinearity. By using the method of penalization argument, we show that there exists a fam…
On the Brezis-Nirenberg type critical problem for nonlinear Choquard equation
Fashun Gao, Minbo Yang
We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation $$-Δu =\left(\int_Ω\frac{|u|^{2_μ^{\ast}}}{|x-y|^μ}dy\right)|u|^{2_μ^{\…
Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in
Claudianor O. Alves, Daniele Cassani, Cristina Tarsi +1
We study the following singularly perturbed nonlocal Schrödinger equation $$ -\vr^2Δu +V(x)u =\vr^{μ-2}\Big[\frac{1}{|x|^μ}\ast F(u)\Big]f(u) \quad \mbox{in} \quad \R^2, $$ where $…
Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity
Claudianor O. Alves, Giovany M. Figueiredo, Minbo Yang
We study the following class of nonlinear Choquard equation, $$ -Δu +V(x)u =\Big( \frac{1}{|x|^μ}\ast F(u)\Big)f(u) \quad \mbox{in} \quad \R^N, $$ where , , is…
Multi-bump solutions for Choquard equation with deepening potential well
Claudianor O. Alves, Alânnio B. Nóbrega, Minbo Yang
We study the existence of multi-bump solutions to Choquard equation $$ \begin{array}{ll} -Δu + (λa(x)+1)u=\displaystyle\big(\frac{1}{|x|^μ}\ast |u|^p\big)|u|^{p-2}u \mbox{ in } \,\…