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January/February 2011 Asymptotic non-degeneracy of the multiple blow-up solutions to the Gel'fand problem in two space dimensions
Massimo Grossi, Hiroshi Ohtsuka, Takashi Suzuki
Adv. Differential Equations 16(1/2): 145-164 (January/February 2011).

Abstract

We consider a sequence of solutions $u_n$ of the problem $$-\Delta u=\lambda e^u \quad \text{in $\Omega$}, \qquad u=0 \quad \text{on $\partial\Omega$},$$ with $\lambda=\{\lambda_n\}_{n\in\mathbb N}$ and blowing up at $m$ points $\kappa_1,\dots,\kappa_m$ in $\Omega$. Under some non-degeneracy assumption on some suitable finite-dimensional function (related to $\kappa_1,\dots,\kappa_m$) we show that $u_n$ is non-degenerate for $n$ large enough.

Citation

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Massimo Grossi. Hiroshi Ohtsuka. Takashi Suzuki. "Asymptotic non-degeneracy of the multiple blow-up solutions to the Gel'fand problem in two space dimensions." Adv. Differential Equations 16 (1/2) 145 - 164, January/February 2011.

Information

Published: January/February 2011
First available in Project Euclid: 18 December 2012

zbMATH: 1227.35091
MathSciNet: MR2766897

Subjects:

Rights: Copyright © 2011 Khayyam Publishing, Inc.

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Vol.16 • No. 1/2 • January/February 2011
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