Published Paper

Inserted: 1 apr 2025
Last Updated: 8 may 2026

Journal: Discrete Contin. Dyn. Syst.
Volume: 53
Pages: 263-286
Year: 2026
Doi: 10.3934/dcds.2025182

Abstract:

We provide a general non-uniqueness result for normalized ground states of nonlinear Schr\"odinger equations with pure power nonlinearity on bounded domains with homogeneous Neumann boundary conditions, defined as global minimizers of the associated energy functional among functions with prescribed mass. Precisely, for nonlinearity powers slightly smaller than the $L^2$-critical exponent, we prove that there always exists at least one value of the mass for which normalized ground states are not unique.