BIRS Workshop Lecture Videos
Non-uniqueness of blowing-up solutions to the Gelfand problem. Grossi, Massimo
I will consider blowing-up solution for the Gelfand problem on planar domains. It is well known that blow up at a single point must occur at a critical point x of a ``reduced functional'' F, whereas uniqueness of blowing up families has been recently shown provided x is a non-degenerate critical point of F. We showed that, if x is a degenerate critical point of F and satisfies some additional generic condition, then one may have two solutions blowing up at the same point. Solutions are constructed using a Lyapunov-Schmidt reduction. This is a joint work with Luca Battaglia and Angela Pistoia.
Item Citations and Data
Attribution-NonCommercial-NoDerivatives 4.0 International