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.File in questo prodotto:
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