preprint

Inserted: 1 apr 2025

Year: 2025

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.