@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 = {2022},
volume = {38},
number = {1},
pages = {1--25},
abstract = {<p style="text-align: justify;">We show that the classical Brezis-Nirenberg problem $$-\Delta u=u|u|+\lambda u \ \ \ \ \ \&nbsp; \ in \&nbsp; \ \&nbsp; \Omega, \\ u=0&nbsp; &nbsp;\&nbsp; \&nbsp; \&nbsp; &nbsp;\&nbsp; \&nbsp; \&nbsp; &nbsp;\&nbsp; \ \ \ \&nbsp; \ \ \ \&nbsp; \&nbsp; \ \&nbsp; \&nbsp; \ \&nbsp; &nbsp; \&nbsp; \ \ on \&nbsp; &nbsp;\&nbsp; \&nbsp; \partial\Omega,$$ 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 $\lambda_0&gt;0.$</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-2020-0044},
url = {https://global-sci.com/article/73750/nodal-solutions-of-the-brezis-nirenberg-problem-in-dimension-6}
}