CERAMATHS - DMATHS seminar: presentation by Matthias Hofmann

The CÉRAMATHS Mathematics Department seminar will welcome Matthias Hofmann (FernUniversität, Hagen, Germany) at 2pm on Thursday, November 27, 2025, for the following talk:

On the existence of Nehari ground states for the Nonlinear Schrödinger Equation on Discrete Graphs

We present results on existence and study properties of standing wave solutions for the nonlinear Schrödinger equation on discrete graphs. We characterize for a self-adjoint realizations of Schrödinger operators conditions related with the geometry of the graph that guarantee discreteness of the spectrum and study ground states on the generalized Nehari manifold in order to prove the existence of standing wave solutions in the self-focusing and defocusing case. In this context, we show properties of the solutions, such as integrability. Furthermore, we discuss the bifurcation of solutions from the trivial solution in this context. The talk is based on a joint work with Setenay Akduman and Sedef Karakılıç.