  We deal with a class of equations driven by nonlocal, possibly degenerate,
integro-differential operators of differentiability order $s\in (0,1)$ and
summability growth $p>1$, whose model is the fractional $p$-Laplacian with
measurable coefficients. We state and prove several results for the
corresponding weak supersolutions, as comparison principles, a priori bounds,
lower semicontinuity, and many others. We then discuss the good definition of
$(s,p)$-superharmonic functions, by also proving some related properties. We
finally introduce the nonlocal counterpart of the celebrated Perron method in
nonlinear Potential Theory.
