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arXiv · 2010.12311

A complete scenario on nodal radial solutions to the Brezis Nirenberg problem in low dimensions

Annalisa Amadori·Francesca Gladiali·Massimo Grossi·Angela Pistoia·Giusi Vaira
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Abstract

In this paper we consider nodal radial solutions of the problem $$ \begin{cases} -Δu=|u|^{2^*-2}u+λu&\text{ in }B,\\ u=0&\text{ on }\partial B \end{cases} $$ where $2^*=\frac{2N}{N-2}$ with $3\le N\le6$ and $B$ is the unit ball of $\R^N$. We compute the asymptotics of the solution $u$ as well as $||u||_\infty$, its first zero and other relevant quantities as $ł$ goes to a critical value $\barł$. Also the sign of $ł-\barł$ is established in all cases. This completes an analogous analysis for $N\ge7$ given in [EGPV].

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Annalisa Amadori, Francesca Gladiali, Massimo Grossi, Angela Pistoia, Giusi Vaira. 2020-10-23. A complete scenario on nodal radial solutions to the Brezis Nirenberg problem in low dimensions. https://doi.org/10.1088/1361-6544%2Fac2a4e

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