par Premoselli, Bruno 
;Thizy, Pierre Damien
Référence Calculus of variations and partial differential equations, 57, 6, 147
Publication Publié, 2018-12-01
;Thizy, Pierre DamienRéférence Calculus of variations and partial differential equations, 57, 6, 147
Publication Publié, 2018-12-01
Article révisé par les pairs
| Résumé : | On any closed manifold (Mn, g) of dimension n∈ { 4 , 5 } we exhibit new blow-up configurations for perturbations of a purely critical stationary Schrödinger equation. We construct positive solutions which blow-up as the sum of two isolated bubbles, one of which concentrates at a point ξ where the potential k of the equation satisfies k(ξ)>n-24(n-1)Sg(ξ),where Sg is the scalar curvature of (Mn, g). The latter condition requires the bubbles to blow-up at different speeds and forces us to work at an elevated precision. We take care of this by performing a construction which combines a priori asymptotic analysis methods with a Lyapounov–Schmidt reduction. |
