Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
In this talk, we consider sign-changing solutions of critical Yamabe-Schrodinger type equations of second order. Unlike their positive counterpart these solutions have no direct physical or geometrical meaning, but have been shown to arise in geometrical contexts. They appear for instance as extremals for higher eigenvalues minimisation (or maximisation) problems in a given conformal class.
We describe in this talk the structure of bubbling sign-changing solutions for these equations and provide a detailed asymptotic description, in strong spaces, of the blow-up. As a consequence we prove some precompactness results for the set of energy-bounded solutions of these equations. Some of these results have been obtained in collaboration with J. Vétois (McGill University).