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
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. https://doi.org/10.57262/ade/1355854333
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