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The logarithmic Choquard equation: sharp asymptotics and nondegeneracy of the groundstate
Denis Bonheure, Silvia Cingolani, Jean Van Schaftingen
We derive the asymptotic decay of the unique positive, radially symmetric solution to the logarithmic Choquard equation $$ - Δu + a u = \frac{1}{2 π} \Bigl[\ln \frac{1}{|x|}* |u|^2…
Multiple positive solutions of the stationary Keller-Segel system
Denis Bonheure, Jean-Baptiste Casteras, Benedetta Noris
We consider the stationary Keller-Segel equation \begin{equation*} \begin{cases} -Δv+v=λe^v, \quad v>0 \quad & \text{in }Ω,\\ \partial_νv=0 &\text{on } \partial Ω, \end{cases} \end…
Multiple radial positive solutions of semilinear elliptic problems with Neumann boundary conditions
Denis Bonheure, Christopher Grumiau, Christophe Troestler
Assuming is a ball in , we analyze the positive solutions of the problem \[ \begin{cases} -Δu+u= |u|^{p-2}u, &\text{ in } B_{R},\newline \partial_νu=0,&\text…