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2000 A uniqueness result for a semilinear elliptic equation in symmetric domains
Massimo Grossi
Adv. Differential Equations 5(1-3): 193-212 (2000).

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.

Citation

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Massimo Grossi. "A uniqueness result for a semilinear elliptic equation in symmetric domains." Adv. Differential Equations 5 (1-3) 193 - 212, 2000.

Information

Published: 2000
First available in Project Euclid: 27 December 2012

zbMATH: 1003.35056
MathSciNet: MR1734541

Subjects:
Primary: 35J65
Secondary: 35J70

Rights: Copyright © 2000 Khayyam Publishing, Inc.

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Vol.5 • No. 1-3 • 2000
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