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arXiv · 2010.09026

Nodal solutions of the Brezis-Nirenberg problem in dimension 6

Angela Pistoia·Giusi Vaira
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Abstract

We show that the classical Brezis-Nirenberg problem $$ -\Delta u=u|u| + \lambda u\ \hbox{in}\ \Omega, u=0\ \hbox{on}\ \partial\Omega, $$ 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 $\lambda_0>0.$

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Angela Pistoia, Giusi Vaira. 2020-10-18. Nodal solutions of the Brezis-Nirenberg problem in dimension 6. https://arxiv.org/abs/2010.09026

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