  We study a nonlinear, nonlocal Dirichlet problem driven by the fractional
p-Laplacian, involving a (p-1)-sublinear reaction. By means of a weak
comparison principle we prove uniqueness of the solution. Also, comparing the
problem to 'asymptotic' weighted eigenvalue problems for the same operator, we
prove a necessary and sufficient condition for the existence of a solution. Our
work extends classical results due to Brezis-Oswald and Diaz-Saa to the
quasilinear nonlocal framework.
