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A Morse index formula for the Lane-Emden problem Ianni, Isabella
Description
We consider the semilinear Lane-Emden problem \begin{equation} \label{problemAbstract} \left\{\begin{array}{lr}-\Delta u= |u|^{p-1}u\qquad \mbox{ in }B\\ u=0\qquad\qquad\qquad\mbox{ on }\partial B \end{array}\right.\tag{$\mathcal E_p$} \end{equation} where $B$ is the unit ball of $\mathbb R^N$, $N\geq3$, centered at the origin and $p\in(1,p_S)$, $p_S=\frac{N+2}{N-2}$. We compute the Morse index of any radial solution $u_p$ of \eqref{problemAbstract}, for $p$ sufficiently close to $p_S$. The proof exploits the asymptotic behavior of $u_p$ as $p\rightarrow p_S$ and the analysis of a limit eigenvalue problem. The result is obtained in collaboration with F. De Marchis and F. Pacella.
Item Metadata
| Title |
A Morse index formula for the Lane-Emden problem
|
| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
| Date Issued |
2016-09-26T09:58
|
| Description |
We consider the semilinear Lane-Emden problem
\begin{equation}
\label{problemAbstract}
\left\{\begin{array}{lr}-\Delta u= |u|^{p-1}u\qquad \mbox{ in }B\\
u=0\qquad\qquad\qquad\mbox{ on }\partial B
\end{array}\right.\tag{$\mathcal E_p$}
\end{equation}
where $B$ is the unit ball of $\mathbb R^N$, $N\geq3$, centered at the origin and $p\in(1,p_S)$, $p_S=\frac{N+2}{N-2}$.
We compute the Morse index of any radial solution $u_p$ of \eqref{problemAbstract}, for $p$ sufficiently
close to $p_S$. The proof exploits the asymptotic behavior of $u_p$
as $p\rightarrow p_S$ and the analysis of a limit eigenvalue problem. The result is obtained in collaboration with F. De Marchis and F. Pacella.
|
| Extent |
37 minutes
|
| Subject | |
| Type | |
| File Format |
video/mp4
|
| Language |
eng
|
| Notes |
Author affiliation: Seconda Università di Napoli
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| Series | |
| Date Available |
2017-03-28
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
| DOI |
10.14288/1.0343366
|
| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
|
| Scholarly Level |
Faculty
|
| Rights URI | |
| Aggregated Source Repository |
DSpace
|
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International