Volume 38, Issue 1
Nodal Solutions of the Brezis-Nirenberg Problem in Dimension 6

Anal. Theory Appl., 38 (2022), pp. 1-25.

Published online: 2021-12

[An open-access article; the PDF is free to any online user.]

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• Abstract

We show that the classical Brezis-Nirenberg problem

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 $\lambda_0>0.$

• Keywords

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

35B44, 58C15

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@Article{ATA-38-1, author = {Angela Pistoia , 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

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} }
TY - JOUR T1 - Nodal Solutions of the Brezis-Nirenberg Problem in Dimension 6 AU - Angela Pistoia , 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 -

We show that the classical Brezis-Nirenberg problem

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 $\lambda_0>0.$

Angela Pistoia & Giusi Vaira. (1970). Nodal Solutions of the Brezis-Nirenberg Problem in Dimension 6. Analysis in Theory and Applications. 38 (1). 1-25. doi:10.4208/ata.OA-2020-0044
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