Wednesday, May 4, 2022 — 2:30 pm — aula M2.2, edificio Matematica
Higher order fractional Schrödinger-Newton systems:
logarithmic kernel vs exponential nonlinearity
Abstract:
We will present recent results for a class of Choquard type equations in the limiting Sobolev dimension in which one has the Riesz logarithmic kernel in the nonlocal convolution and where the nonlinearity exhibits the highest possible growth, which is of exponential type. The competition between the logarithmic kernel and the exponential nonlinearity demands for new tools. A proper function space setting is provided by a new weighted version of the Pohozaev-Trudinger inequality which enables us to prove the existence of variational, in particular finite energy solutions.