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arXiv · 2207.11199

Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods

Abdelrazek Dieb·Isabella Ianni·Alberto Saldaña
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Abstract

We consider positive solutions of a fractional Lane-Emden type problem in a bounded domain with Dirichlet conditions. We show that uniqueness and nondegeneracy hold for the asymptotically linear problem in general domains. Furthermore, we also prove that all the known uniqueness and nondegeneracy results in the local case extend to the nonlocal regime when the fractional parameter s is sufficiently close to 1.

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Abdelrazek Dieb, Isabella Ianni, Alberto Saldaña. 2022-07-22. Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods. https://arxiv.org/abs/2207.11199

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