On the logistic equation for the fractional p‐Laplacian

Abstract

AbstractWe 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.