A general theorem for the construction of blowing-up solutions to some elliptic nonlinear equations with Lyapunov-Schmidt's finite-dimensional reduction

Frédéric Robert (1) , Jérôme Vétois (2)

1 IECL - Institut Élie Cartan de Lorraine
2 JAD - Laboratoire Jean Alexandre Dieudonné

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; blow-up; Nonlinear elliptic equations

Domaines: Equations aux dérivées partielles [math.AP]

Frédéric Robert, Jérôme Vétois. A general theorem for the construction of blowing-up solutions to some elliptic nonlinear equations with Lyapunov-Schmidt's finite-dimensional reduction. Concentration Analysis and Applications to PDE (ICTS Workshop, Bangalore, January2012), Birkhäuser, pp.85-116, 2013, Trends in Mathematics, ⟨10.1007/978-3-0348-0373-1_6⟩. ⟨hal-00936337⟩