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 con- venient 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.

On the logistic equation for the fractional p-Laplacian

Iannizzotto A.
;
2023-01-01

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 con- venient 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.
2023
Bifurcation; Comparison principle; Fractional ��-Laplacian; Logistic equation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/354404
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