Standing waves for discrete Schrodinger equations in infinite lattices with saturable nonlinearities

In this paper, we consider the periodic discrete nonlinear equation [GRAPHICS] where L is a Jacobi operator, and the nonlinearities g(n)(s) are asymptotically linear as |s| -> infinity. In the two different cases (omega is a spectral endpoint of L, or it belongs to a finite spectral gap of L), we obtain the existence of nontrivial solitons of this equation by using variational methods. In particular, a necessary and sufficient condition is obtained for the existence of gap solitons of the nonlinear equation. Here, solitons appear when we look for standing waves of some discrete nonlinear Schrodinger equations. (C) 2016 Elsevier Inc. All rights reserved.