Uniqueness of the critical point for semi-stable solution in ${\mathbb{R}}^2$

Fabio De Regibus, Massimo Grossi, Debangana Mukherjee

In this paper we show the uniqueness of the critical point for \emph{semi-stable} solutions of the problem $$\begin{cases} -Δu=f(u)&\text{in }Ω\\ u>0&\text{in }Ω\\ u=0&\text{on } \…