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math.AP2021
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…
math.AP2021★ 1 cited
Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two
Massimo Grossi, Isabella Ianni, Peng Luo +1
We are concerned with the Lane-Emden problem \begin{equation*} \begin{cases} -Δu=u^{p} &{\text{in}~Ω},\\[0.5mm] u>0 &{\text{in}~Ω},\\[0.5mm] u=0 &{\text{on}~\partial Ω}, \end{cases…