Scalar curvatures of manifolds of negative conformal invariant

In this paper, we are interested in the problem of prescribing the scalar curvature on a compact riemannian manifold of negative conformal invariant. We give a necessary and sufficient condition when the prescribed function f is nonpositive. When sup(f) > 0, we merely find a sufficient condition. This is the subject of the first theorem. In the second one, we prove the multiplicity of the solutions of subcritical (for the Sobolev imbeddings) elliptic equations. In another article [8], we will prove the multiplicity of the solutions of the prescribing curvature problem, i.e. for a critical elliptic equation.