We prove the Lazer-McKenna conjecture for the superlinear elliptic problem of the Ambrosetti-Prodi type with a non-homogeneous non-linearity by constructing solutions with sharp peaks. We also compute the critical groups provided the critical points are isolated.
"On the superlinear Lazer-McKenna conjecture: the non-homogeneous case." Adv. Differential Equations 12 (9) 961 - 993, 2007.