1
Return

GROUND STATES FOR THE DEFOCUSING NONLINEAR SCHRODINGER EQUATION ON NON-COMPACT METRIC GRAPHS

delete2026-03-01
delete0
PRE
AI
D
Durand-simonnet, Elio *
S
Shakarov, Boris
DOI：10.3934/cpaa.2026029delete
deleteOriginal
deleteOriginal request for help
deleteShare
deleteSave
Abstract

Abstract

En 中文
We investigate the existence and stability of ground states for the defocusing nonlinear Schrodinger equation on non-compact metric graphs. We establish a sharp criterion for the existence of action ground states in terms of the spectral properties of the underlying Hamiltonian: ground states exist if and only if the bottom of the spectrum is negative and the frequency lies within a suitable range. We further explore the relation between action and energy ground states, showing that while every action minimizer yields an energy minimizer, the converse fails in general. In particular, we prove that energy ground states may not exist for arbitrary masses. This discrepancy is illustrated through explicit examples on star graphs with delta and delta '-type vertex conditions: in the mass-sub critical case, we exhibit a large interval of masses for which no energy minimizer exists, whereas in the supercritical regime, energy ground states exist for all masses.
Keywords:
Nonlinear Schrodinger equation
standing waves
action ground state
energy ground state
nonlinear quantum graphs

Journal

C
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
IF:
0.9
Papers:
88
Citations:
0

Organization

U
universite de toulouse (epe)
Scholars:
177
Papers: 93
Citations: 0
Cited Papers

Cited Papers

Citing Papers

Citing Papers