  We study the Cauchy problem for non-linear non-local operators that may be
degenerate. Our general framework includes cases where the jump intensity is
allowed to depend on the values of the solution itself, e.g. the porous medium
equation with the fractional Laplacian and the parabolic fractional
$p$-Laplacian. We show the existence, uniqueness of bounded solutions and study
their further properties. Several new examples of non-local, non-linear
operators are provided.
