Existence of discrete solitons in discrete nonlinear Schrodinger equations with non-weak couplings

Discrete solitons are spatially localized periodic solutions in the discrete nonlinear Schrodinger equation. The anti-integrable limit is defined for the discrete nonlinear Schrodinger equation as the limit of vanishing couplings. There are an infinite number of trivial discrete solitons in this limit, each of which consists of a finite number of excited sites. The existence of discrete solitons continued from them has been proved only for sufficiently weak couplings. In the present paper, we focus on the case of non-weak couplings and prove the existence of discrete solitons over an explicitly given range of the coupling constant.