8 citations · 8 across the 7 of their papers we have counts for
7 papers
Quantitative analysis of ground states for the fractional logarithmic Schrödinger equation
Xiaoming An, Shuangjie Peng, Fulin Zhong
Let and . We study positive ground states of the fractional logarithmic Schrödinger equation \begin{equation*} (-Δ)^sQ=Q\log Q \quad\text{in }\mathbb{R}^N. \end{equ…
Qualitative analysis of energy ground states for magnetic focusing Gross-Pitaevskii equations
Xiaoming An, Lun Guo, Xiao Luo +1
We prove the uniqueness, asymptotics, symmetry, and orbital stability of energy ground states for 3D magnetic Gross-Pitaevskii equations under mild conditions on the electric poten…
Semiclassical states for fractional logarithmic Schrödinger equations
Xiaoming An
In this paper, we consider the following fractional logarithmic Schrödinger equation \begin{equation*} \varepsilon^{2s}(-Δ)^s u + V(x)u=u\log |u|^2\ \ \text{in}\ \R^N, \end{equatio…
Semi-classical analysis for Fractional Schrödinger Equations with fast decaying potenials
Xiaoming An, Lipeng Duan, Yanfang Peng
We study the following fractional Schrödinger equation \begin{equation*}\label{eq0.1} ε^{2s}(-Δ)^s u + V(x)u = |u|^{p - 2}u, \,\,x\in\,\,\mathbb{R}^N, \end{equation*} where $s\in (…
Nonstandard solutions for a perturbed nonlinear Schrödinger system with small coupling coefficients\protect\thanks{A perturbed nonlinear Schrödinger system
Xiaoming An, Chunhua Wang
In this paper, we consider the following weakly coupled nonlinear Schrödinger system \begin{equation*} \left\{ \begin{array}{ll} -ε^{2}Δu_1 + V_1(x)u_1 = |u_1|^{2p - 2}u_1 + β|u_1|…
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…