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 - <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>