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.

On the logistic equation for the fractional p-Laplacian

Iannizzotto A.
;
Mosconi S.;
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 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.
2023
bifurcation
comparison principle
fractional p-Laplacian
logistic equation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/623531
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