| Abstract: |
| On a closed manifold $(M^n,g)$ of dimension $n \in \{4,5\}$ we construct new blow-up configurations for perturbations of a purely critical stationary Schr\odinger equation. We construct positive solutions which blow-up as the sum of two bubbles, where the highest one concentrates at a point $\xi$ where the potential $k$ of the equation lies above the geometric threshold of the scalar curvature. This condition requires the bubbles to blow-up at very different speeds. To take care of this we perform a construction which combines a priori asymptotic analysis methods with a Lyapounov-Schmidt reduction. |
|