We prove the Lazer-McKenna conjecture for an elliptic problem of Ambrosetti-Prodi type with critical and supercritical nonlinearities by constructing solutions concentrating on higher dimensional manifolds, under some partially symmetric assumption on the domain.
"On the Lazer-McKenna Conjecture Involving Critical and Super-critical Exponents." Methods Appl. Anal. 15 (1) 97 - 120, March 2008.