A Morse inequality for a fourth order elliptic equation on a bounded domain

摘要

This article deals with the existence of multiple solutions of a fourth order elliptic equation with a critical nonlinearity on a bounded domain of Rn,n≥5Rn,n≥5. We develop an approach to overcome the lack of compactness of the problem and we establish under a generic hypothesis a Morse inequality providing a lower bound of the number of solutions.