### A uniqueness result for a semilinear elliptic equation in symmetric domains

Massimo Grossi

#### Abstract

We prove that the problem $$\begin{cases} -\Delta u=u^p\quad & \text{in \Omega}\\ u>0\quad & \text{in \Omega } \\ u=0\quad & \text{on \partial\Omega} \end{cases}$$ has only one solution if $\Omega$ is a convex symmetric domain of $\Bbb R^N$, $N\ge3$ and $p <{{N+2}\over{N-2}}$ is close to ${{N+2}\over{N-2}}$. Moreover, we show that this solution is nondegenerate.

#### Article information

Source
Adv. Differential Equations, Volume 5, Number 1-3 (2000), 193-212.

Dates
First available in Project Euclid: 27 December 2012

Mathematical Reviews number (MathSciNet)
MR1734541

Zentralblatt MATH identifier
1003.35056

#### Citation

Grossi, Massimo. A uniqueness result for a semilinear elliptic equation in symmetric domains. Adv. Differential Equations 5 (2000), no. 1-3, 193--212. https://projecteuclid.org/euclid.ade/1356651383