Martin Mayer, Chaona Zhu
The problem of prescribing conformally the scalar curvature on a closed Riemannian manifold of negative Yamabe invariant is always solvable, when the function [Formula: see text] to be prescribed is strictly negative, while sufficient and necessary conditions are known for [Formula: see text]. For sign changing [Formula: see text] Rauzy [Courbures scalaires des variétés d’invariant conforme négatif, Trans. Amer. Math. Soc. 347(12) (1995) 4729–4745] showed solvability, provided [Formula: see text] is not too positive. We revisit this problem in a different variational context, thereby recovering and quantifying the principal existence result of Rauzy and show under additional assumptions, that for a sign changing [Formula: see text] solutions to the conformally prescribed scalar curvature problem, while existing, are not unique.