no code implementations • 26 Feb 2021 • Annalisa Amadori, Francesca De Marchis, Isabella Ianni
We compute the Morse index $\textsf{m}(u_{p})$ of any radial solution $u_{p}$ of the semilinear problem: \begin{equation} \label{problemaAbstract}\tag{P} \left\{ \begin{array}{lr} -\Delta u=|x|^{\alpha}|u|^{p-1}u & \mbox{in } B\\ u=0 & \mbox{ on }\partial B \end{array} \right.
Analysis of PDEs
no code implementations • 18 Feb 2021 • Massimo Grossi, Isabella Ianni, Peng Luo, Shusen Yan
We are concerned with the Lane-Emden problem \begin{equation*} \begin{cases} -\Delta u=u^{p} &{\text{in}~\Omega},\\[0. 5mm] u>0 &{\text{in}~\Omega},\\[0. 5mm] u=0 &{\text{on}~\partial \Omega}, \end{cases} \end{equation*} where $\Omega\subset \mathbb R^2$ is a smooth bounded domain and $p>1$ is sufficiently large.
Analysis of PDEs
