In this paper we obtain results on existence of standing waves in Discrete Nonlinear Shrödinger equation (DNLS) with saturable nonlinearity on a two-dimensional lattice. We consider two types of solutions: with periodic amplitude and vanishing at infinity (localized solution). Sufficient conditions for the existence of such solutions are obtained with the aid of Nehari manifold and periodic approximations.
"Existence of Standing Waves in DNLS with Saturable Nonlinearity on 2D-Lattice." Commun. Math. Anal. 22 (2) 18 - 34, 2019.