Multiple solutions for the scalar curvature problem on the sphere

Abstract

We study the existence of solutions for the prescribed scalar curvature problem on Sn with n ≥ 3. We prove that given an arbitrary K0 ∈ C2(Sn), K0 > 0, any positive ϵ, any α in (0, 1), and any integer l we can find such that and the equation has at least l solutions.