Abstract
This paper is concerned with the excitation threshold for the ground state in the coupled discrete nonlinear Schrödinger lattice system. Excitation threshold is characterized by the variational methods. We establish the existence of the excitation threshold connected with the dimensionality d of the lattice. We prove that if d ⩾ 2, then the excitation threshold exists and the ground state exists if and only if the total power is greater than the excitation threshold. The compactness of the minimizing sequence follows by the concentration compactness principle. We also prove the upper estimates on the excitation threshold and the frequency of the ground state.
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