28. November 2023
Giulio Romani (Università degli studi di Milano-Bicocca)
Schrödinger-Poisson systems in Sobolev limiting cases
Systems which couple a Schrödinger and a Poisson equation arise in several physical contexts such as quantum mechanics and electromagnetism. When considered in the whole space and in the limiting case for the Sobolev embeddings, one can deal with exponentially growing nonlinearities, but the application of standard variational tools is spoiled by the fact that the Riesz kernel of the Poisson equation is logarithmic, hence unbounded from above and below.
In this framework, I will present some existence results about local SP-systems in the case of zero mass, and nonlocal SP-systems, by means of a variational approximating procedure for auxiliary Choquard equations, where the logarithmic Riesz kernel is uniformly approximated by polynomial kernels.This talk is based on joint works with Daniele Cassani (University of Insubria) and Zhisu Liu (Wuhan University).