Calculus of Variations and Geometric Measure Theory

D. Bartolucci - A. Jevnikar - Y. Lee - W. Yang

Local uniqueness of $m$-bubbling sequences for the Gel'fand equation

created by jevnikar on 10 Apr 2018
modified on 21 Jan 2019


Accepted Paper

Inserted: 10 apr 2018
Last Updated: 21 jan 2019

Journal: Comm. PDEs
Year: 2018


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.