The purpose of this paper is to study a class of discrete nonlinear Schrödinger equations. Under a weak superlinearity condition at infinity instead of the classical Ambrosetti-Rabinowitz condition, the existence of standing waves of the equations is obtained by using the Nehari manifold approach.
"On Standing Wave Solutions for Discrete Nonlinear Schrödinger Equations." Abstr. Appl. Anal. 2013 (SI61) 1 - 6, 2013. https://doi.org/10.1155/2013/436919