## Advances in Differential Equations

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

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

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1356651383

**Mathematical Reviews number (MathSciNet)**

MR1734541

**Zentralblatt MATH identifier**

1003.35056

**Subjects**

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations

Secondary: 35J70: Degenerate elliptic equations

#### 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