152 citations · 377 across the 16 of their papers we have counts for
16 papers
Uniqueness, Nondegeneracy, and Asymptotic Expansions of Ground States for the Dirac-Coulomb System
Pan Chen, Qi Guo, Xiaoyu Zeng
We study ground states of the following Dirac-Coulomb system $$\mathscr{D}_cu_c- \left(\abs{x}^{-1}\ast \abs{u_c}^2\right)u_c=ω_cu_c,$$ under the constraint $\norm[L^2]{u_c}^2=1.$F…
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…
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}\|…
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(…
The Lieb-Yau Conjecture for Ground States of Pseudo-Relativistic Boson Stars
Yujin Guo, Xiaoyu Zeng
It is known that ground states of the pseudo-relativistic Boson stars exist if and only if the stellar mass satisfies , where the finite constant is called the c…
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…
Ground States of Two-Component Attractive Bose-Einstein Condensates II: Semi-trivial Limit Behavior
Yujin Guo, Shuai Li, Juncheng Wei +1
As a continuation of [14], we study new pattern formations of ground states for two-component Bose-Einstein condensates (BEC) with homogeneous trapping potentials in $R…
Ground States of Two-Component Attractive Bose-Einstein Condensates I: Existence and Uniqueness
Yujin Guo, Shuai Li, Juncheng Wei +1
We study ground states of two-component Bose-Einstein condensates (BEC) with trapping potentials in , where the intraspecies interaction and the interspecies int…
Existence and Uniqueness of Normalized Solutions for the Kirchhoff equation
Xiaoyu Zeng, Yimin Zhang
For a class of Kirchhoff functional, we first give a complete classification with respect to the exponent for its -normalized critical points, and show that the minimizer…
Existence and asymptotic behavior for the ground state of quasilinear elliptic equation
Xiaoyu Zeng, Yimin Zhang
In this paper, we are concerned with the existence and asymptotic behavior of minimizers for a minimization problem related to some quasilinear elliptic equations. Firstly, we prov…
Cylindrically Symmetric Ground State Solutions for Curl-Curl Equations with Critical Exponent
Xiaoyu Zeng
We study the following nonlinear critical curl-curl equation \begin{equation}\label{eq0.1}\nabla\times \nabla\times U +V(x)U=|U|^{p-2}U+ |U|^4U,\quad x\in \mathbb{R}^3,\end{equatio…
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…