Accepted Paper

Inserted: 10 apr 2018
Last Updated: 21 jan 2019

Journal: Comm. PDEs
Year: 2018

Abstract:

We consider the Gel'fand problem, $\Delta w_{\varepsilon}+\varepsilon^2he^{w_{\varepsilon}}=0$ in $\Omega$, $w_{\varepsilon}=0$ on $\partial\Omega,$ where $h$ is a nonnegative function in ${\Omega\subset\mathbb{R}^2}$. Under suitable assumptions on $h$ and $\Omega$, we prove the local uniqueness of $m-$bubbling solutions for any $\varepsilon>0$ small enough.

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