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.
Bounded Palais-Smale sequences with Morse type information for some constrained functionals
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abstract
In this paper, we study, for functionals having a mountain pass geometry on a constraint, the existence of bounded Palais-Smale sequences carrying Morse index type information.
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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.