  The well-known Ambrosetti-Prodi theorem considers perturbations of the
Dirichlet Laplacian by a nonlinear function whose derivative jumps over the
principal eigenvalue of the operator. Various extensions of this landmark
result were obtained for self-adjoint operators, in particular by Berger and
Podolak, who gave a geometrical description of the solution set. In this text
we show that similar theorems are valid for non self-adjoint operators. In
particular, we prove that the semilinear operator is a global fold. As a
consequence, we obtain what appears to be the first exact multiplicity result
for elliptic equations in non-divergence form. We employ techniques based on
the maximum principle.
