Filippo Boni – Thursday 16 April 2026

Speaker: Filippo Boni (Politecnico di Torino)

Title: On the Stationary NLS Equation with a Point Interaction

Abstract:

In this talk, we present recent results, obtained in spatial dimensions two and three, on the existence and characterization of stationary solutions to nonlinear Schrödinger (NLS) equations with focusing power-type nonlinearities in the presence of a point interaction.

We prove the existence of particular solutions, known as ground states, which are positive, radially symmetric, decreasing in the radial variable, and exhibit a singularity proportional to the Green’s function. We then establish a connection between stationary solutions to NLS equations with point interactions and singular solutions to semilinear elliptic equations. As an application, in dimension two we prove the existence of infinitely many singular nodal solutions to semilinear elliptic equations.

These results were obtained in collaboration with Riccardo Adami and Lorenzo Tentarelli (Politecnico di Torino), Raffaele Carlone and Raffaele Scandone (Università degli Studi di Napoli “Federico II”), Matteo Gallone (Università degli Studi di Milano Statale) and Diego Noja (Università degli Studi di Milano-Bicocca).