Nonlocal ODE, conformal geometry and applications.

We study radially symmetric solutions for a semilinear equation with fractional Laplacian. Contrary to the local case, where we can give a solution to an ODE by simply looking at its phase portrait, in the nonlocal case we develop several new methods. We will give some applications, in particular to the existence of solutions of the singular fractional Yamabe problem, and the uniqueness of steady states of aggregation-diffusion equations.Non UBCUnreviewedAuthor affiliation: Universidad Autonoma de MadridFacult