The number of positive solutions to the Brezis-Nirenberg problem

19 Aug 2020 Cao Daomin Luo Peng Peng Shuangjie

In this paper we are concerned with the well-known Brezis-Nirenberg problem \begin{equation*} \begin{cases} -\Delta u= u^{\frac{N+2}{N-2}}+\varepsilon u, &{\text{in}~\Omega},\\ u>0, &{\text{in}~\Omega},\\ u=0, &{\text{on}~\partial \Omega}. \end{cases} \end{equation*} The existence of multi-peak solutions to the above problem for small $\varepsilon>0$ was obtained by Musso and Pistoia... (read more)

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