On a fractional Nirenberg problem on n-dimensional spheres: Existence and multiplicity results

Abstract

In this paper, we consider a fractional Nirenberg type problem involving σ-exponent of the Laplacian on the standard n-dimensional spheres Sn. We prove existence and multiplicity result under β-flatness condition, n−2σ<β<n. In particular, we give a new existence criterium which generalizes the previous results of [22] and [23] for σ∈(0,1) and recovers the already known result for the classical case σ=1.