On the logistic equation for the fractional p-Laplacian

Iannizzotto A.

;Mosconi S.;Papageorgiou N. 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 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.