108 citations · 155 across the 23 of their papers we have counts for
24 papers
Multiple positive solutions with prescribed masses for a coupled Schrödinger system: mass mixed and Sobolev critical coupled case
Qing Guo, Qihan He, Wei Shuai +1
The aim of this paper is to establish multiple positive normalized solutions to the following coupled Schröding…
Bivariate Hardy-Sobolev Inequality and Its Sharp Stability
Yingfang Zhang, Xuexiu Zhong, Wenming Zou
This paper establishes a bivariate Hardy-Sobolev inequality. Let () be an open domain, , , with , and $κ\i…
Normalized solutions for critical Choquard systems
Hui Zhang, Jianjun Zhang, Xuexiu Zhong
In this paper, we consider the critical Choquard system with prescribed mass \begin{equation*} \begin{aligned} \left\{ \begin{array}{lll} -Δu+λ_1u=(I_μ\ast |u|^{2^*_μ})|u|^{2^*_μ-2…
Normalized solutions for a Kirchhoff type equations with potential in
Leilei Cui, Qihan He, Zongyan Lv +1
In the present paper, we study the existence of normalized solutions to the following Kirchhoff type equations \begin{equation*} -\left(a+b\int_{\R^3}|\nabla u|^2\right)Δu+V(x)u+λu…
The existence of positive solution for an elliptic problem with critical growth and logarithmic perturbation
Yinbin Deng, Qihan He, Yiqing Pan +1
We consider the existence and nonexistence of positive solution for the following Brézis-Nirenberg problem with logarithmic perturbation: \begin{equation*} \begin{cases} -Δu={\left…
Normalized solutions to Kirchhoff type equations with a critical growth nonlinearity
Jian Zhang, Jianjun Zhang, Xuexiu Zhong
In this paper, we are concerned with normalized solutions of the Kirchhoff type equation \begin{equation*} -M\left(\int_{\R^N}|\nabla u|^2\mathrm{d} x\right)Δu = λu +f(u) \ \ \math…
Existence and Concentration Results for the General Kirchhoff Type Equations
Yinbin Deng, Wei Shuai, Xuexiu Zhong
We consider the following singularly perturbed Kirchhoff type equations $$-\varepsilon^2 M\left(\varepsilon^{2-N}\int_{\R^N}|\nabla u|^2 dx\right)Δu +V(x)u=|u|^{p-2}u~\hbox{in}~\R^…
Localized semiclassical states for Hamiltonian elliptic systems in dimension two
Hui Zhang, Minbo Yang, Jianjun Zhang +1
In this paper, we consider the Hamiltonian elliptic system in dimension two\begin{equation}\label{1.5}\aligned \left\{ \begin{array}{lll} -ε^2Δu+V(x)u=g(v)\ & \text{in}\quad \mathb…
Bifurcation from essential spectrum for an elliptic equation with general nonlinearity
Jianjun Zhang, Xuexiu Zhong, Huansong Zhou
In this paper, based on some prior estimates, we show that the essential spectrum is a bifurcation point for an superlinear elliptic equation with only local conditions, whic…
On the Kirchhoff equation with prescribed mass and general nonlinearities
Xiaoyu Zeng, Jianjun Zhang, Yimin Zhang +1
In the present paper, we apply a global branch approach to study the existence, non-existence and multiplicity of positive normalized solutions $(λ_c, u_c)\in \mathbb{R}\times H^1(…
A global branch approach to normalized solutions for the Schrödinger equation
Louis Jeanjean, Jianjun Zhang, Xuexiu Zhong
We study the existence, non-existence and multiplicity of prescribed mass positive solutions to a Schrödinger equation of the form \begin{equation*} -Δu+λu=g(u), \quad u \in H^1(\m…
Normalized solution to the Schödinger equation with potential and general nonlinear term: Mass super-critical case
Yanheng Ding, Xuexiu Zhong
In present paper, we prove the existence of solutions to the following Schrödinger equation $$ \begin{cases} -Δu(x)+V(x)u(x)+λu(x)=g(u(x))\quad &\hbo…
Positive normalized solution to the Kirchhoff equation with general nonlinearities of mass super-critical
Qihan He, Zongyan Lv, Yimin Zhang +1
In present paper, we study the normalized solutions to the following Kirchhoff problem $$ -\left(a+b\int_{\R^N}|\nabla u|^2dx\right)Δu+λu=g(u)~\h…
Normalized solutions for nonlinear Schrödinger systems with special mass-mixed terms: The linear couple case
Zhen Chen, Xuexiu Zhong, Wenming Zou
In this paper, we prove the existence of positive solutions to the following coupled Schrödinger system $$\begin{cases} -Δu + λ_1 u=…
A new deduce of the strict binding inequality and its application: Ground state normalized solution to Schrödinger equations with potential
Xuexiu Zhong, Wenming Zou
In the present paper, we prove the existence of solutions to the following elliptic equations with potential $\displaystyle -Δu+(V(x)+λ)u=g(u)\;\hbox…
Sharp interaction estimates and their application: existence of normalized ground states to coupled Schrödinger systems with potentials
Yinbin Deng, Qihan He, Xuexiu Zhong
In this paper, our aim is to prove the existence of normalized ground state for the following Schrödinger systems with potentials $$\begin{cases} -Δu_1+V_1(x)u_1+λ_1 u_1=\partial_1…
Normalized solutions for a coupled Schrödinger system
Thomas Bartsch, Xuexiu Zhong, Wenming Zou
In the present paper, we prove the existence of solutions to systems of coupled Schrödinger equations $$ \begin{…
On a double-variable inequality and elliptic systems involving critical Hardy-Sobolev exponents
Xuexiu Zhong, Wenming Zou
Let () be an open domain which is not necessarily bounded. The sharp constant and extremal functions to the following kind of double-variable inequ…
Existence of extremal functions for a family of Caffarelli-Kohn-Nirenberg inequalities
Xuexiu Zhong, Wenming Zou
Consider the following inequalities due to Caffarelli, Kohn and Nirenberg {\it (Compositio Mathematica,1984):} $$\Big(\int_Ω\frac{|u|^r}{|x|^s}dx\Big)^{\frac{1}{r}}\leq C(p,q,r,μ,σ…
On Elliptic Systems involving critical Hardy-Sobolev exponents (Part II)
Xuexiu Zhong, Wenming Zou
This paper is the second part of a work devoted to the study of elliptic systems involving multiple Hardy-Sobolev critical exponents: $$\begin{cases} -Δu-λ\frac{|u|^{2^*(s_1)-2}u}{…
A nonlinear elliptic PDE with multiple Hardy-Sobolev critical exponents in
Xuexiu Zhong, Wenming Zou
In this paper, we will study the following PDE in involving multiple Hardy-Sobolev critical exponents: $$ \begin{cases} Δu+\sum_{i=1}^{l}λ_i \frac{u^{2^*(s_i)-1}}{|x…
On Elliptic Systems involving critical Hardy-Sobolev exponents
Xuexiu Zhong, Wenming Zou
Let () be an open domain which is not necessarily bounded. By using variational methods, we consider the following elliptic systems involving multiple Hard…
A perturbed nonlinear elliptic PDE with two Hardy-Sobolev critical exponents
Xuexiu Zhong, Wenming Zou
Let be a open bounded domain in () with . Suppose that is at and the mean curvature of at is negati…
On coupled Schrödinger systems with double critical exponents and indefinite weights
Xuexiu Zhong, Wenming Zou
By using variational methods, we study the existence of mountain pass solution to the following doubly critical Schrödinger system: $$ \begin{cases} -Δu-μ_1\frac{u}{|x|^2}-|u|^{2^{…