On a fourth order elliptic equation with critical nonlinearity in dimension six

Abstract

This paper is devoted to the study of the following nonlinear elliptic problem: Δ 2 u = Ku 5 , u > 0 in Ω , u = Δ u = 0 on ∂ Ω , where K is a positive function and Ω is a bounded and smooth domain in R 6 . We prove a version of Morse Lemma at infinity for this problem. Using this Morse Lemma at infinity, we characterize the critical points at infinity of the associated functional and we give an existence result.