Construction of blow-up sequences for the prescribed scalar curvature equation on $$S^n$$ S n . III. Aggregated and towering blow-ups

Abstract

Using annular domains introduced in Part II (Leung, Calc Var PDE 46:1–29, 2013), we present constructive results on blow-up sequences of infinite number of solutions for the (prescribed and fixed) conformal scalar curvature equation on \(S^n\) (\(n\ge 6\)), including aggregated and towering blow-ups. The constructions make use of the Lyapunov–Schmidt reduction method, and count on the hyperbolic structure on the collection of standard bubbles.