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This analysis identifies non-uniqueness of normalized ground states in nonlinear Schrödinger equations, suggesting complexities in Neumann boundary conditions.
We provide a general non-uniqueness result for normalized ground states of nonlinear Schrödinger 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 L²-critical exponent, we prove that there always exists at least one value of the mass for which normalized ground states are not unique.
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Dovetta et al. (2025) studied this question.
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