Large conformal metrics with prescribed scalar curvature

In the general case, if in addition we assume that there exists a non-degenerate conformal metric g0=u04n−2g, with u0>0, whose scalar curvature is equal to h, then there exists a bounded family of conformal metrics g0,λ=u0,λ4n−2g, with u0,λ>0, which satisfies u0,λ→u0 uniformly as λ→0. Here, we build a second family of “bubbling” metrics gλ, where uλ blows up at the point ξ and approaches u0 far from ξ as λ goes to zero. In particular, this shows that this problem admits more than one solution.