Monday, March 17, 2025 - 14:00 in V2-205
Second radial eigenfunctions to a fractional Dirichlet problem and uniqueness for a semilinear equation
A talk in the Nonlocal Equations: Analysis and Numerics series by
Tobias Weth from Frankfurt am Main
| Abstract: |
In this talk, I will report on joint work with Moustapha Fall on the shape of
radial second Dirichlet eigenfunctions of fractional Schrödinger type oper-
ators in the unit ball B with a nondecreasing radial potential. Specifically,
we show that the eigenspace corresponding to the second radial eigenvalue
is simple and spanned by an eigenfunction which changes sign precisely
once in the radial variable and has a nonvanishing fractional boundary
derivative. We apply this result to prove uniqueness and nondegeneracy of
positive ground state solutions to a semilinear fractional Dirichlet problem
in B. If time permits, I will also address the uniqueness within the class
of arbitrary positive solutions and the corresponding problem in the entire
space.
Within the CRC this talk is associated to the project(s): A7 |
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