152 citations · 523 across the 18 of their papers we have counts for
18 papers
Uniqueness of Single Peak Solutions for Coupled Nonlinear Gross-Pitaevskii Equations with Potentials
Xiaoyu Zeng, Huan-Song Zhou
For a couple of singularly perturbed Gross-Pitaevskii equations, we first prove that the single peak solutions, if they concentrate on the same point, are unique provided that the…
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…
A constrained minimization problem related to two coupled pseudo-relativistic Hartree equations
Wenqing Wang, Xiaoyu Zeng, Huan-Song Zhou
We are concerned with the following constrained minimization problem: $$e(a_{1},a_{2},β) := \inf\left\{E_{a_{1},a_{2},β}(u_{1},u_{2}): \|u_{1}\|_{L^{2}(\mathbb{R}^{3})} = \|u_{2}\|…
Properties of the minimizers for a constrained minimization problem arising in Kirchhoff equation
Helin Guo, Huan-Song Zhou
Let and be a coercive function in . We study the following constrained minimization problem on a suitable weighted Sobolev space : \…
Infinitely many solutions for a Schrodinger equation with sign-changing potential and nonlinear term
Long-Jiang Gu, Huan-Song Zhou
We propose a new variational approach to finding multiple critical points for strongly indefinite problems without assuming the weak upper semicontinuity on the variational functio…
Blow-up behavior of ground states for a nonlinear Schrödinger system with attractive and repulsive interactions
Yujin Guo, Xiaoyu Zeng, Huan-Song Zhou
We consider a nonlinear Schrödinger system arising in a two-component Bose-Einstein condensate (BEC) with attractive intraspecies interactions and repulsive interspecies interactio…
Blow-up solutions for a Kirchhoff type elliptic equation with trapping potential
Helin Guo, Yimin Zhang, Huan-Song Zhou
We study a generalized Kirchhoff type equation with trapping potential. The existence and blow-up behavior of solutions with normalized L2-norm for this problem are discussed.
An Improved Fountain Theorem and its Application
Long-Jiang Gu, Huan-Song Zhou
The main aim of the paper is to prove a fountain theorem without assuming the -upper semicontinuity condition on the variational functional. Using this improved fountain theorem…
A variational problem arising in registration of diffusion tensor images
Huan Han, Huan-Song Zhou
The existence of a global minimizer for a variational problem arising in registration of diffusion tensor images is proved, which ensures that there is a regular spatial transforma…
Eigenvalue problem for a p-Laplacian equation with trapping potentials
Long-Jiang Gu, Xiaoyu Zeng, Huan-Song Zhou
Consider the following eigenvalue problem of p-Laplacian equation \begin{equation}\label{P} -Δ_{p}u+V(x)|u|^{p-2}u=μ|u|^{p-2}u+a| u|^{s-2}u, x\in \mathbb{R}^{n}, \tag{P} \end{equat…
Blow-up solutions for two coupled Gross-Pitaevskii equations with attractive interactions
Yujin Guo, Xiaoyu Zeng, Huan-Song Zhou
The paper is concerned with a system of two coupled time-independent Gross-Pitaevskii equations in , which is used to model two-component Bose-Einstein condensates wi…
Properties of ground states of attractive Gross-Pitaevskii equations with multi-well potentials
Yujin Guo, Zhi-Qiang Wang, Xiaoyu Zeng +1
We are interested in the attractive Gross-Pitaevskii (GP) equation in , where the external potential vanishes on disjoint bounded domains $Ω_i\subset \R^2\ (i=1,2,…
Energy estimates and symmetry breaking in attractive Bose-Einstein condensates with ring-shaped potentials
Yujin Guo, Xiaoyu Zeng, Huan-Song Zhou
This paper is concerned with the properties of -normalized minimizers of the Gross-Pitaevskii (GP) functional for a two-dimensional Bose-Einstein condensate with attractive in…
Concentration behavior of standing waves for almost mass critical nonlinear Schrödinger equations
Yujin Guo, Xiaoyu Zeng, Huan-Song Zhou
We study the following nonlinear Schrödinger equation where and is some type…
Schrödinger-Poisson equations with singular potentials in
Yongsheng Jiang, Huan-Song Zhou
The existence and estimate of positive solutions are discussed for the following Schrödinger-Poisson system {ll} -Δu +(λ+\frac{1}{|y|^α})u+ϕ(x) u =|u|^{p-1}u, x=(y,z)\…
Multiple solutions for a nonhomogeneous Schrödinger-Maxwell system in
Yongsheng Jiang, Zhengping Wang, Huan-Song Zhou
The paper considers the following nonhomogeneous Schrödinger-Maxwell system -Δu + u+λϕ(x) u =|u|^{p-1}u+g(x),\ x\in \mathbb{R}^3, -Δϕ= u^2, \ x\in \mathbb{R}^3, . \leqno{(SM)} wher…
Schrodinger-Poisson system with steep potential well
Yongsheng Jiang, Huan-Song Zhou
We study the following Schrödinger-Poisson system (P_λ)\{ll} -Δu + (1+μg(x))u+λϕ(x) u =|u|^{p-1}u, x\in \mathbb{R}^3,
Bound states for a stationary nonlinear Schrodinger-Poisson system with sign-changing potential in
Yongsheng Jiang, Huan-Song Zhou
We study the following Schrödinger-Poisson system (P_λ){ll} -Δu + V(x)u+λϕ(x) u =Q(x)u^{p}, x\in \mathbb{R}^3 \\ -Δϕ= u^2, \lim\limits_{|x|\to +\infty}ϕ(x)=0, u>0, where $λ\geqslan…