Jérôme Vétois (McGill University)

Title:Compactness of sign-changing solutions to critical elliptic equations with bounded negative part
Abstract: In this talk, we will look at the question of compactness of sign-changing solutions to a class of critical elliptic Schrödinger equations on a closed Riemannian manifold. We will present a sharp compactness result for the set of sign-changing solutions with bounded negative part. We obtained this result in dimensions greater than or equal to 7 when the potential function is below the geometric threshold of the conformal Laplacian. The whole set of sign-changing solutions is non-compact in general. We will also discuss constructions of counterexamples in the case of the sphere in dimensions less than or equal to 6 and for potentials above the geometric threshold in higher dimensions. This is a joint work with Bruno Premoselli (ULB, Bruxelles).