Phase spaces and periodic solutions of set functional dynamic equations with infinite delay Original Research Article

Very recently, a new theory known as set dynamic equations on time scales has been built. In this paper, a phase space is built for set functional dynamic equations with infinite delay on time scales and sufficient criteria are established for the existence of periodic solutions of such equations, which generalize and incorporate as special cases some known results for set differential equations and for set difference equations when the time scale is the real number set or the integer set, respectively, moreover, for differential inclusions and difference inclusions if the variable under consideration is a single valued mapping. Our results show that one can unify the study of some continuous or discrete problems in the sense of (set) dynamic equations on general time scales.