  We consider a Dirichlet type 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.
