Abstract
We study Schrödinger–Newton equations with general power nonlinearity on the lattice Z d . After the proof of well-posedness of the Cauchy problem, our interest is focused on the existence of stable standing (stationary) solutions. Employing variational methods we prove the existence of a ground state solution solving the associated stationary system. Orbital stability as well as exponential localization of the ground state is verified. Finally, we discuss the existence of excitation thresholds for ground state solutions in dependence of the conserved mass ( l 2 -norm).
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