Work

Nonuniqueness of normalized ground states for nonlinear Schrödinger equations on metric graphs

Year: 2025

Type: article

Abstract: We establish general nonuniqueness results for normalized ground states of nonlinear Schrödinger equations with power nonlinearity on metric graphs. Basically, we show that, whenever in the ‐subcritical regime a graph hosts ground states at every mass, for nonlinearity powers close to the ‐critical exponent , there is at least one value of the mass for which ground states are nonunique. As a consequence, we also show that, for all such graphs and nonlinearities, there exist action ground states that are not normalized ground states.

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms.70025

Author: Simone Dovetta

Institution: Politecnico di Torino

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Ministero dell'Università e della Ricerca, NextGenerationEU