Nodal Solutions of the Brezis-Nirenberg Problem in Dimension 6

Year:    2022

Author:    Angela Pistoia, Giusi Vaira

Analysis in Theory and Applications, Vol. 38 (2022), Iss. 1 : pp. 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 $\lambda_0>0.$

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-2020-0044

Analysis in Theory and Applications, Vol. 38 (2022), Iss. 1 : pp. 1–25

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Sign-changing solutions blow-up phenomenon Lyapunov-Schmidt reduction Transversality theorem.

Author Details

Angela Pistoia

Giusi Vaira