On the logistic equation for the fractional p‐Laplacian

Antonio Iannizzotto, Sunra Mosconi and Nikolaos S. Papageorgiou

Mathematische Nachrichten, 2023, vol. 296, issue 4, 1451-1468

Abstract: We consider a Dirichlet problem for a nonlinear, nonlocal equation driven by the degenerate fractional p‐Laplacian, with a logistic‐type reaction depending on a positive parameter. In the subdiffusive and equidiffusive cases, we prove existence and uniqueness of the positive solution when the parameter lies in convenient intervals. In the superdiffusive case, we establish a bifurcation result. A new strong comparison result, of independent interest, plays a crucial role in the proof of such bifurcation result.

Date: 2023
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https://doi.org/10.1002/mana.202100025

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