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.
Weinstein, Lyapunov stability of ground states of nonlinear dispersiv e evolution equations , Comm
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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.