1 citations · 2 across the 4 of their papers we have counts for
5 papers
Positive solutions for a critical elliptic equation
Lipeng Duan, Shuying Tian
In this paper, we are concerned with the following elliptic equation \begin{equation*} \begin{cases} -Δu= Q(x)u^{2^*-1 }+\varepsilon u^{s},~ &{\text{in}~Ω},\\[1mm] u>0,~ &{\text{in…
New type of solutions for the Nonlinear Schrödinger Equation in
Lipeng Duan, Monica Musso
We construct a new family of entire solutions for the nonlinear Schrödinger equation \begin{align*} \begin{cases} -Δu+ V(y ) u = u^p, \quad u>0, \quad \text{in}~ \mathbb{R}^N, \\[2…
Clustering of Boundary Interfaces for an inhomogeneous Allen-Cahn equation on a smooth bounded domain
Lipeng Duan, Suting Wei, Jun Yang
We consider the inhomogeneous Allen-Cahn equation $$ ε^2Δu\,+\,V(y)(1-u^2)\,u\,=\,0\quad \mbox{in}\ Ω, \qquad \frac {\partial u}{\partial ν}\,=\,0\quad \mbox{on}\ \partial Ω, $$ wh…
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 (…
On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau system
Lipeng Duan, Jun Yang
For the following Ginzburg-Landau system in \begin{align*} \begin{cases} -Δw^+ +\Big[A_+\big(|w^+|^2-{t^+}^2\big)+B\big(|w^-|^2-{t^-}^2\big)\Big]w^+=0, \\[3mm] -Δw^…