A General Theorem for the Construction of Blowing-up Solutions to Some Elliptic Nonlinear Equations via Lyapunov–Schmidt’s Finite-dimensional Reduction
Résumé
Abstract. We prove a general finite-dimensional reduction theorem for critical
equations of scalar curvature type. Solutions of these equations are constructed
as a sum of peaks. The use of this theorem reduces the proof of
existence of multi-peak solutions to some test-functions estimates and to the
analysis of the interactions of peaks.