Pullback attractors and invariant measures for discrete Klein-Gordon-Schrödinger equations

In this article, we first provide a sufficient and necessary condition for the existence of a pullback-D attractor for the process defined on a Hilbert space of infinite sequences. As an application, we investigate the non-autonomous discrete Klein-Gordon-Schrödinger system of equations, prove the existence of the pullback-D attractor and then the existence of a unique family of invariant Borel probability measures associated with the considered system.