Conformal metrics with prescribed fractional Q-curvatures on the standard n-dimensional sphere

Abstract

We are interested to the problem of finding conformal metrics with prescribed fractional Q-curvatures of order 2σ on the n-dimensional standard sphere Sn,n≥2. By studying the lack of compactness of the problem for all σ∈(0,n2), we provide existence results. Our main assumption is the so called “non-degeneracy condition”.