Ricerc@Sapienza

. We investigate the solvability of the Ambrosetti-Prodi problem
for the p-Laplace operator $Delta_p$ with Venttsel' boundary conditions on a two-dimensional
open bounded set with Koch-type boundary, and on an open
bounded three-dimensional cylinder with Koch-type fractal boundary. Using a
priori estimates, regularity theory and a sub-supersolution method, we obtain
a necessary condition for the non-existence of solutions (in the weak sense), and
the existence of at least one globally bounded weak solution. Moreover, under
additional conditions, we apply the Leray-Schauder degree theory to obtain
results about multiplicity of weak solutions.