A General Theorem for the Construction of Blowing-up Solutions to Some Elliptic Nonlinear Equations via Lyapunov–Schmidt’s Finite-dimensional Reduction

Frédéric Robert (1) , Jérôme Vétois (2)

1 IECN - Institut Élie Cartan de Nancy
2 JAD - Laboratoire Jean Alexandre Dieudonné

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.

Mots clés: conformal invariance; Nonlinear elliptic equations; blow-up

Domaines: Equations aux dérivées partielles [math.AP]; Géométrie différentielle [math.DG]

Frédéric Robert, Jérôme Vétois. A General Theorem for the Construction of Blowing-up Solutions to Some Elliptic Nonlinear Equations via Lyapunov–Schmidt’s Finite-dimensional Reduction. Concentration Compactness and Profile Decompositions, Jan 2012, Bangalore, India. pp.85-116. ⟨hal-01097287⟩