  For Dirichlet boundary conditions on a bounded domain, what happens to the
critical set of the Ambrosetti-Prodi operator if the nonlinearity is only a
Lipschitz map? It turns out that many properties which hold in the smooth case
are preserved, despite of the fact that the operator is not even differentiable
at some points. In particular, a global Lyapunov-Schmidt decomposition of great
convenience for numerical inversion is still available.
