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math.AP2020★ 1 cited
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…
math.AP2020
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…