Advances in Differential Equations

A uniqueness result for a semilinear elliptic equation in symmetric domains

Massimo Grossi

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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.


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