TY - JOUR T1 - Nodal Solutions of the Brezis-Nirenberg Problem in Dimension 6 AU - Pistoia , Angela AU - Vaira , Giusi JO - Analysis in Theory and Applications VL - 1 SP - 1 EP - 25 PY - 2021 DA - 2021/12 SN - 38 DO - http://doi.org/10.4208/ata.OA-2020-0044 UR - https://global-sci.org/intro/article_detail/ata/20010.html KW - Sign-changing solutions, blow-up phenomenon, Lyapunov-Schmidt reduction, Transversality theorem. AB -

We show that the classical Brezis-Nirenberg problem $$-\Delta u=u|u|+\lambda u \ \ \ \ \ \  \ in \  \ \  \Omega, \\ u=0   \  \  \   \  \  \   \  \ \ \ \  \ \ \ \  \  \ \  \  \ \    \  \ \ on \   \  \  \partial\Omega,$$ when $\Omega$ is a bounded domain in $\mathbb R^6$ has a sign-changing solution which blows-up at a point in $\Omega$ as $\lambda$ approaches a suitable value $\lambda_0>0.$