M. Fall

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math.AP2025

Second radial eigenfunctions to a fractional Dirichlet problem and uniqueness for a semilinear equation

Mouhamed Moustapha Fall, Tobias Weth

We analyze the shape of radial second Dirichlet eigenfunctions of fractional SchrÃ¶dinger type operators of the form $(- I^)^{s} + V$ in the unit ball $B$ in $R^{N}$ with a nond…

math.AP2025

Overdetermined problems with fractional Laplacian

Mouhamed Moustapha Fall, Sven Jarohs

Let $N \geq 1$ and $s \in (0, 1)$ . In the present work we characterize bounded open sets $I^c ◯$ with $C^{2}$ boundary (\textit{not necessarily connected}) for which the following overdet…

math.AP2024

Nondegeneracy properties and uniqueness of positive solutions to a class of fractional semilinear equations

Mouhamed Moustapha Fall, Tobias Weth

We prove that positive solutions $u \in H^{s} (R^{N})$ to the equation $(- I^)^{s} u + u = u^{p}$ in $R^{N}$ are nonradially nondegenerate, for all $s \in (0, 1)$ , $N \geq 1$ and $p…