Proves existence of spatially exponentially localized time-periodic ground states in d-dimensional discrete NLS with delta potential and power nonlinearity, with explicit lower excitation thresholds for focusing cases and upper thresholds for defocusing cases, plus scattering below threshold.
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Minimizers on the Pohozaev-Nehari manifold for the L²-supercritical Schrödinger-Poisson equation with general nonlinearity f are unique and radially symmetric up to translations.
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Nonlinear discrete Schr\"odinger equations with a point defect
Proves existence of spatially exponentially localized time-periodic ground states in d-dimensional discrete NLS with delta potential and power nonlinearity, with explicit lower excitation thresholds for focusing cases and upper thresholds for defocusing cases, plus scattering below threshold.
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On uniqueness and radiality of minimizers to $L^2$ supercritical Schr\"{o}dinger Poisson equations with general nonlinearities
Minimizers on the Pohozaev-Nehari manifold for the L²-supercritical Schrödinger-Poisson equation with general nonlinearity f are unique and radially symmetric up to translations.