For mass-supercritical nonlinearities with an external potential, positive normalized solutions exist on sufficiently large star-shaped domains and, under a radial condition on the potential, in R^N.
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Normalized Solutions on large smooth domains to the Schr\"{o}dinger equation with potential and general nonlinearity: Mass super-critical case
For mass-supercritical nonlinearities with an external potential, positive normalized solutions exist on sufficiently large star-shaped domains and, under a radial condition on the potential, in R^N.