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

Abstract

This article deals with the existence of multiple solutions of a fourth order elliptic equation with a critical nonlinearity on a bounded domain of $\mathbb{R}^n, n\geq 5$. 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.

Keywords

• fourth order pde
• critical nonlinearity
• variational problem
• critical points at infinity