On the lack of bound states for certain NLS equations on metric graphs

TL;DR

This paper investigates the conditions under which bound states do not exist for nonlinear Schrödinger equations on noncompact metric graphs, emphasizing the influence of graph topology and metric properties.

Contribution

It provides new results on the nonexistence of bound states for NLS equations on certain metric graphs, extending previous discussions.

Findings

Bound states are absent under specific topological conditions.

Graph properties critically influence the existence of bound states.

Results complete prior research on NLS equations on metric graphs.

Abstract

The purpose of this paper is to prove some results on the absence of bound states for certain nonlinear Schr\"odinger equations on noncompact metric graphs with localized nonlinearity. In particular, we show how the topological and metric properties of graphs affect the existence/nonexistence of bound states. This work completes the discussion initiated in [17, 18].