Statistical solution and Kolmogorov entropy for the impulsive discrete Klein-Gordon-Schrödinger-type equations

This paper studies the impulsive discrete Klein-Gordon-Schrödinger-type equations. We first prove that the problem of the discrete Klein-Gordon-Schrödinger-type equations with initial and impulsive conditions is global well-posedness. Then we establish that the solution operators form a continuous process and that this process possesses a pullback attractor and a family of invariant Borel probability measures. Further, we prove that this family of Borel probability measures satisfies the Liouville type theorem piecewise and is a statistical solution of the impulsive discrete Klein-Gordon-Schrödinger-type equations. Finally, we formulate the concept of Kolmogorov entropy for the statistical solution and estimate its upper bound.