@Article{ATA-38-1, author = {Pistoia , Angela and Vaira , Giusi}, title = {Nodal Solutions of the Brezis-Nirenberg Problem in Dimension 6}, journal = {Analysis in Theory and Applications}, year = {2021}, volume = {38}, number = {1}, pages = {1--25}, abstract = {

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 $\lambda_0>0.$

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2020-0044}, url = {http://global-sci.org/intro/article_detail/ata/20010.html} }