7 citations · 28 across the 17 of their papers we have counts for
17 papers
Extremal values of -Pohozaev manifolds and their applications
Taicheng Liu, Yuanze Wu
In this paper, we consider the following Schrödinger equation: \begin{equation*} \begin{cases} -Δu=λu+μ|u|^{q-2}u+|u|^{2^*-2}u\quad\text{in }\mathbb{R}^N,\\ \int_{\mathbb{R}^N}|u(x…
Stability of the Caffarelli-Kohn-Nirenberg inequality: the existence of minimizers
Juncheng Wei, Yuanze Wu
In this paper, we consider the following variational problem: \begin{eqnarray*} \inf_{u\in D^{1,2}_a(\bbr^N)\backslash\mathcal{Z}}\frac{\|u\|^2_{D^{1,2}_a(\bbr^N)}-C_{a,b,N}^{-1}\|…
Infinitely many nonradial positive solutions for multi-species nonlinear Schrödinger systems in
Tuoxin Li, Juncheng Wei, Yuanze Wu
In this paper, we consider the multi-species nonlinear Schrödinger systems in $\bbr^N$: \begin{equation*} \left\{\aligned&-Δu_j+V_j(x)u_j=μ_ju_j^3+\sum_{i=1;i\not=j}^dβ_{i,j} u_i^2…
Sharp stability of the logarithmic Sobolev inequality in the critical point setting
Juncheng Wei, Yuanze Wu
In this paper, we consider the Euclidean logarithmic Sobolev inequality \begin{eqnarray*} \int_{\mathbb{R}^d}|u|^2\log|u|dx\leq\frac{d}{4}\log\bigg(\frac{2}{πd e}\|\nabla u\|_{L^2(…
Positive solutions of the Gross-Pitaevskii equation for energy critical and supercritical nonlinearities
D. E. Pelinovsky, J. Wei, Y. Wu
We consider positive and spatially decaying solutions to the Gross-Pitaevskii equation with a harmonic potential. For the energy-critical case, there exists a ground state if and o…
Normalized solutions for Schrödinger equations with critical Sobolev exponent and mixed nonlinearities
Juncheng Wei, Yuanze Wu
In this paper, we consider the following nonlinear Schrödinger equations with mixed nonlinearities: \begin{eqnarray*} \left\{\aligned &-Δu=λu+μ|u|^{q-2}u+|u|^{2^*-2}u\quad\text{in…
Ground states of Nonlinear Schrödinger System with Mixed Couplings
Juncheng Wei, Yuanze Wu
We consider the following -coupled nonlinear Schrödinger system: \begin{align*} \begin{cases} &-Δu_j + λ_j u_j = μ_j u_j^3 + \sum_{i=1, i\not=j}^k β_{i,j} u_i^2 u_j \quad {\rm i…
Spikes of the two-component elliptic system in $\bbr^4$ with Sobolev critical exponent
Yuanze Wu, Wenming Zou
Consider the following elliptic system: \begin{equation*} \left\{\aligned&-\ve^2Δu_1+λ_1u_1=μ_1u_1^3+α_1u_1^{p-1}+βu_2^2u_1\quad&\text{in}Ω,\\ &-\ve^2Δu_2+λ_2u_2=μ_2u_2^3+α_2u_2^{p…
On a critical Kirchhoff problem in high dimensions
Yisheng Huang, Zeng Liu, Yuanze Wu
In this paper, we consider the following Kirchhoff problem $$ \left\{\aligned -\bigg(a+b\int_Ω|\nabla u|^2dx\bigg)Δu&= λu^{q-1} + μu^{2^*-1}, &\quad \text{in }Ω, \\ u&>0,&\quad\tex…
Positive solutions to an elliptic equation in of the Kirchhoff type
Yisheng Huang, Zeng Liu, Yuanze Wu
In this paper, we consider the following Kirchhoff type problem $$\left\{\aligned&-\biggl(a + b\int_{\mathbb{R}^N} |\nabla u|^2 dx \biggr) Δu + V(x) u = |u|^{p-2}u &\text{ in } \ma…
On finding solutions of a Kirchhoff type problem
Yisheng Huang, Zeng Liu, Yuanze Wu
Consider the following Kirchhoff type problem $$ \left\{\aligned -\bigg(a+b\int_{\mathbb{B}_R}|\nabla u|^2dx\bigg)Δu&= λu^{q-1} + μu^{p-1}, &\quad \text{in}\mathbb{B}_R, \\ u&>0,&\…
On Kirchhoff type equations with critical Sobolev exponent and Naimen's open problems
Yisheng Huang, Zeng Liu, Yuanze Wu
We study the following Brezis-Nirenberg problem of Kirchhoff type $$ \left\{\aligned &-(a+b\int_Ω|\nabla u|^2dx)Δu = λ|u|^{q-2}u + δ|u|^{2}u, &\quad \text{in}\ Ω, \\ &u=0,& \text{o…
On a Kirchhoff type problems with potential well and indefinite potential
Yuanze Wu, Yisheng Huang, Zeng Liu
In this paper, we study the following Kirchhoff type problem:% $$ \left\{\aligned&-\bigg(α\int_{\bbr^3}|\nabla u|^2dx+1\bigg)Δu+(λa(x)+a_0)u=|u|^{p-2}u&\text{ in }\bbr^3,\\% &u\in\…
On a biharmonic equations with steep potential well and indefinite potential
Yisheng Huang, Zeng Liu, Yuanze Wu
In this paper, we study the following biharmonic equations:% $$ \left\{\aligned&Δ^2u-a_0Δu+(λb(x)+b_0)u=f(u)&\text{ in }\bbr^N,\\% &u\in\h,\endaligned\right.\eqno{(\mathcal{P}_λ)}%…
On a doubly critical Schrödinger system in $\bbr^4$ with steep potential wells
Yuanze Wu, Wenming Zou
Study the following two-component elliptic system% \begin{equation*} \left\{\aligned&Δu-(λa(x)+a_0)u+u^3+βv^2u=0\quad&\text{in }\bbr^4,\\% &Δv-(λb(x)+b_0)v+v^3+βu^2v=0\quad&\text{i…
On a two-component Bose-Einstein condensate with steep potential wells
Yuanze Wu, Tsung-fang Wu, Wenming Zou
In this paper, we study the following two-component systems of nonlinear Schrödinger equations \begin{equation*} \left\{\aligned&Δu-(λa(x)+a_0(x))u+μ_1u^3+βv^2u=0\quad&\text{in }\b…
On the Schrödinger-Poisson system with steep potential well and indefinite potential
Juntao Sun, Tsung-fang Wu, Yuanze Wu
In this paper, we study the following Schrödinger-Poisson system: $$ \left\{\aligned&-Δu+V_λ(x)u+K(x)ϕu=f(x,u)&\quad\text{in }\bbr^3,\\ &-Δϕ=K(x)u^2&\quad\text{in }\bbr^3,\\ &(u,ϕ)…