Pullback Attractors And Invariant Measures For Discrete Klein-Gordon-Schr(?)dinger Equations And Discrete Long-wave-short-wave Resonance Equations

This master thesis mainly studies the existence of a pullback at-tractors and invariant measures for discrete klein-gordon-schr(?)dinger equations and discrete long-wave-short-wave resonance equations on a Banach space of infinite sequences.First,we investigate the unique ex-istence and boundedness solution of the problem.Next,we present a sufficient and necessary condition for the existence of a pullback attrac-tor for the process defined by general lattice system.Moreover,if the conditions hold,then the continuous process has a pullback attractor.Finally,we apply the result of Lukazewicz and Robinson to prove pro-cess is ?-continuous and existence of a unique family of invariant Borel probability measures associated with the process.