Lazer-McKenna conjecture: The critical case

Citations of this article
Mendeley users who have this article in their library.


We consider an elliptic problem of Ambrosetti-Prodi type involving critical Sobolev exponent on a bounded smooth domain of dimension six or higher. By constructing solutions with many sharp peaks near the boundary of the domain, but not on the boundary, we prove that the number of solutions for this problem is unbounded as the parameter tends to infinity, thereby proving the Lazer-McKenna conjecture in the critical case. © 2006 Elsevier Inc. All rights reserved.




Wei, J., & Yan, S. (2007). Lazer-McKenna conjecture: The critical case. Journal of Functional Analysis, 244(2), 639–667.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free