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.