A compactness type result for Paneitz-Branson operators with critical nonlinearity

Abstract

Given (M,g), a compact Riemannian manifold of dimension n \ge 8, we consider positive solutions uα of Δ²gu - divg(Aα du) + aα u = u2\sharp-1, where Aα is a smooth, symmetric (2,0) tensor and aα a smooth function. Assuming that Aα and aα converge in a suitable sense as α → \infty, we obtain conditions under which the weak limit of uα is nontrivial.