Speaker
Description
In this talk, we investigate existence and nonexistence of positive and nodal action ground states for the nonlinear Schrödinger equation on metric graphs.
For noncompact graphs with finitely many edges, we detect purely topological sharp conditions preventing the existence of ground states or of nodal ground states. We also investigate analogous conditions of metrical nature. The negative results are complemented by several sufficient conditions to ensure existence, either of topological or metrical nature, or a combination of the two.
This is based on joint work with Simone Dovetta (Politecnico di Torino (Italy)), Damien Galant (UPHF and UMons (Belgium)), Enrico Serra (Politecnico di Torino (Italy)), Christophe Troestler (UMons (Belgium)).
