© 2015 Elsevier Inc. This paper is devoted to the study of positive radial solutions of the scalar curvature equation, i.e. Δu(x) + K(|x|)uσ-1(x) = 0 where σ = 2n/n-2and we assume that K(|x|) = k(|x|ε) and k(r) ∈ C1is bounded and ε > 0 is small. It is known that we have at least a ground state with fast decay for each positive critical point of k for ε small enough. In fact if the critical point k(r0) is unique and it is a maximum we also have uniqueness; surprisingly we show that if k(r0)is a minimum we have an arbitrarily large number of ground stateswith fast decay. The results are obtained using Fowler transformation and developing a dynamical approach inspired by Melnikov theory. We emphasize that the presence of subharmonic solutions arising from zeroes of Melnikov functions has not appeared previously, as far as we are aware.