On the notion of ground state for nonlinear Schrödinger equations on metric graphs

We compare ground states for the nonlinear Schrödinger equation on metric graphs, defined as global minimizers of the action functional constrained on the Nehari manifold, and least action solutions, namely minimizers of the action among all solutions to the equation. In principle, four alternative...

Full description

Saved in:
Bibliographic Details
Published in:Calculus of variations and partial differential equations Vol. 62; no. 5; p. 159
Main Authors: De Coster, Colette, Dovetta, Simone, Galant, Damien, Serra, Enrico
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2023
Springer Nature B.V
Springer Verlag
Subjects:
Analysis
Analysis of PDEs
Calculus of Variations and Optimal Control; Optimization
Constraints
Control
Graphs
Ground state
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Schrodinger equation
Systems Theory
Theoretical
35Q55
35R02
58E30
49J40
least action
AMS Subject Classification: 35R02
ground states
constrained minimization
58E30 nonlinear Schrödinger
AMS Subject Classification: 35R02 35Q55 49J40 58E30 nonlinear Schrödinger ground states least action constrained minimization
ISSN:0944-2669, 1432-0835
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We compare ground states for the nonlinear Schrödinger equation on metric graphs, defined as global minimizers of the action functional constrained on the Nehari manifold, and least action solutions, namely minimizers of the action among all solutions to the equation. In principle, four alternative cases may take place: ground states do exist (thus coinciding with least action solutions); ground states do not exist while least action solutions do; both ground states and least action solutions do not exist and the levels of the two minimizing problems coincide; both ground states and least action solutions do not exist and the levels of the two minimizing problems are different. We show that in the context of metric graphs all four alternatives do occur. This is accomplished by a careful analysis of doubly constrained variational problems. As a by-product, we obtain new multiplicity results for positive solutions on a wide class of noncompact metric graphs.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-023-02497-4