Periodic Solutions Of Functional Dynamic Equations With Infinite Delay On Time Scales

In this paper, sufficient criteria are established for the existence of periodic solutions of some functional dynamic equations with infinite delays on time scales, which generalize and incorporate as special cases many known results for differential equations and for difference equations when the time scale T is set to be R or Z, respectively. The approach is mainly based on the Krasnoselskii fixed point theorem, which has been extensively applied in studying existence problems in differential equations and difference equations but rarely applied in dynamic equations on time scales. This study shows that one can unify such existence studies in the sense of dynamic equations on general time scales.