76 citations · 250 across the 26 of their papers we have counts for
26 papers
Axial Symmetry of Normalized Solutions for Magnetic Gross-Pitaevskii Equations with Anharmonic Potentials
Yujin Guo, Yan Li, Yong Luo +1
This paper is concerned with normalized solutions of the magnetic focusing Gross-Pitaevskii equations with anharmonic potentials in , where or . We construct…
Existence of Boundary Layers for the supercritical Lane-Emden Systems
Qing Guo, Junyuan Liu, Shuangjie Peng
We consider the following supercritical problem for the Lane-Emden system: \begin{equation}\label{eq00} \begin{cases} -Δu_1=|u_2|^{p-1}u_2\ &in\ D,\\ -Δu_2=|u_1|^{q-1}u_1 \ &in\ D,…
Sign-changing solutions to the slightly supercritical Lane-Emden system with Neumann boundary conditions
Qing Guo, Shuangjie Peng
We consider the following slightly supercritical problem for the Lane-Emden system with Neumann boundary conditions: \begin{equation*} \begin{cases} -Δu_1=|u_2|^{p_ε-1}u_2,\ &in\ Ω…
Semi-classical states for fractional Choquard equations with decaying potentials
Yinbin Deng, Shuangjie Peng, Xian Yang
This paper deals with the following fractional Choquard equation where $\varep…
Existence and decays of solutions for fractional Schrödinger equations with decaying potentials
Yinbin Deng, Shuangjie Peng, Xian Yang
We revisit the following fractional Schrödinger equation \begin{align}\label{1a} \varepsilon^{2s}(-Δ)^su +Vu=u^{p-1},\,\,\,u>0,\ \ \ \mathrm{in}\ \R^N, \end{align} where $\varepsil…
Qualitative analysis for Moser-Trudinger nonlinearities with a low energy
Peng Luo, Kefan Pan, Shuangjie Peng
We are concerned with the Moser-Trudinger problem \begin{equation*} \begin{cases} -Δu=λue^{u^2}~~&\mbox{in}~Ω,\\[0.5mm] u>0 ~~ &{\text{in}~Ω},\\[0.5mm] u=0~~&\mbox{on}~\partial Ω,…
The -convergence at the Neumann boundary for Liouville equations
Yuchen Bi, Jiayu Li, Lei Liu +1
In this paper, we study the blow-up analysis for a sequence of solutions to the Liouville type equation with exponential Neumann boundary condition. For interior case, i.e. the blo…
Existence and non-degeneracy of positive multi-bubbling solutions to critical elliptic systems of Hamiltonian type
Qing Guo, Junyuan Liu, Shuangjie Peng
This paper deals with the following critical elliptic systems of Hamiltonian type, which are variants of the critical Lane-Emden systems and analogous to the prescribed curvature p…
Non-degeneracy and existence of new solutions for the Schrödinger equations
Yuxia Guo, Monica Musso, Shuangjie Peng +1
We consider the following nonlinear problem $$ (P) \quad \quad - Δu + V(|y|)u=u^{p},\quad u>0 \quad \mbox{in} \ {\mathbb{R}}^N, \quad u \in H^1({\mathbb{R}}^N), $$ where is…
Existence and Asymptotic Behavior of Ground States for Rotating Bose-Einstein Condensates
Yujin Guo, Yong Luo, Shuangjie Peng
We study ground states of two-dimensional Bose-Einstein condensates with repulsive () or attractive () interactions in a trap rotating at the velocity . It is…
Local Uniqueness of Ground States for Rotating Bose-Einstein Condensates with Attractive Interactions
Yujin Guo, Yong Luo, Shuangjie Peng
We study ground states of two-dimensional Bose-Einstein condensates with attractive interactions in a trap rotating at the velocity . It is known that there exist a criti…
The number of positive solutions to the Brezis-Nirenberg problem
Daomin Cao, Peng Luo, Shuangjie Peng
In this paper we are concerned with the well-known Brezis-Nirenberg problem \begin{equation*} \begin{cases} -Δu= u^{\frac{N+2}{N-2}}+\varepsilon u, &{\text{in}~Ω},\\ u>0, &{\text{i…
Excited states on Bose-Einstein condensates with attractive interactions
Peng Luo, Shuangjie Peng, Shusen Yan
We study the Bose-Einstein condensates (BEC) in two or three dimensions with attractive interactions, described by constraint Gross-Pitaevskii energy functional. First, we…
Multi-peak semiclassical bound states for Fractional Schrödinger Equations with fast decaying potentials
Xiaoming An, Shuangjie Peng
We study the following fractional Schrödinger equation \begin{equation*}\label{eq0.1} \varepsilon^{2s}(-Δ)^s u + V(x)u = f(u), \,\,x\in\mathbb{R}^N, \end{equation*} where $s\in(0,1…
Semi-classical Solutions For Fractional Schrodinger Equations With Potential Vanishing At Infinity
Xiaoming An, Shuangjie Peng, Chaodong Xie
We study the following fractional Schrödinger equation \begin{equation}\label{eq0.1} \varepsilon^{2s}(-Δ)^s u + Vu = |u|^{p - 2}u,\ \ x\in\,\,\mathbb{R}^N. \end{equation} We show t…
Multi-peak positive solutions to a class of Kirchhoff equations
Peng Luo, Shuangjie Peng, Chunhua Wang +1
In the present paper, we consider the nonlocal Kirchhoff problem \begin{eqnarray*} -\left(ε^2a+εb\int_{\mathbb{R}^{3}}|\nabla u|^{2}\right)Δu+V(x)u=u^{p},\,\,\,u>0 & & \text{in }\m…
Existence, non-degeneracy of proportional positive solutions and least energy solutions for a fractional elliptic system
QiHan He, Shuangjie Peng, Yan-Fang Peng
In this paper, we study the following fractional nonlinear Schrödinger system $$ \left\{% \begin{array}{ll} (-Δ)^s u +u=μ_1 |u|^{2p-2}u+β|v|^p|u|^{p-2}u,~~x\in \R^N,\vspace{2mm}\\…
Uniqueness of planar vortex patch in incompressible steady flow
Daomin Cao, Yuxia Guo, Shuangjie Peng +1
We investigate a steady planar flow of an ideal fluid in a bounded simple connected domain and focus on the vortex patch problem with prescribed vorticity strength. There are two m…
Uniqueness and Nondegeneracy of positive solutions to Kirchhoff equations and its applications in singular perturbation problems
Gongbao Li, Peng Luo, Shuangjie Peng +2
In the present paper, we establish the uniqueness and nondegeneracy of positive energy solutions to the Kirchhoff equation \begin{eqnarray*} -\left(a+b\int_{\mathbb{R}^{3}}|\nabla…
Uniqueness of positive solutions with Concentration for the Schrödinger-Newton problem
Peng Luo, Shuangjie Peng, Chunhua Wang
We are concerned with the following Schrödinger-Newton problem \begin{equation} -\varepsilon^2Δu+V(x)u=\frac{1}{8π\varepsilon^2} \big(\int_{\mathbb R^3}\frac{u^2(ξ)}{|x-ξ|}dξ\big)u…
Uniqueness and nondegeneracy of positive solutions to a class of Kirchhoff equations in
Gongbao Li, Shuangjie Peng, Chang-Lin Xiang
In this paper, we establish a type of uniqueness and nondegeneracy results for positive solutions to the following nonlocal Kirchhoff equations \begin{eqnarray*} -\left(a+b\int_{\m…
Existence and local uniqueness of bubbling solutions for poly-harmonic equations with critical growth
Yuxia Guo, Shuangjie Peng, Shusen Yan
\begin{abstract} We consider the following poly-harmonic equations with critical exponents: \begin{equation}\label{P} (-Δ)^m u =K(y)u^{\frac{N+2m}{N-2m}},\;\;\; u>0\;\;\;\hbox{in}…
Infinitely many positive solutions for nonlinear fractional Schrödinger equations
Wei Long, Shuangjie Peng, Jing Yang
We consider the following nonlinear fractional Schrödinger equation where is a positive radial function, ,…
Segregated Vector Solutions for linearly coupled Nonlinear Schrödinger Systems
Chang-Shou Lin, Shuangjie Peng
We consider the following system linearly coupled by nonlinear Schrödinger equations in $$ \left\{\begin{array}{ll} -Δu_j+u_j=u^3_j-\va\sum\limits_{i\neq j}^N u_i,\{1cm}& x\…