Almost Periodic Dynamic Equations Under Matched Spaces

Abstract

AbstractIn this chapter, based on the theory of δ-almost periodic functions and n 0-order Δ-almost periodic functions developed in Chap. 4, some fundamental results of the δ-almost periodic solutions and n 0-order Δ-almost periodic solutions of a general dynamic equations are established under matched spaces of time scales. Particularly, the basic results of almost periodic problems of the q-dynamic equations on a quantum time scale are included as the special case. In Sects. 7.1–7.3, by using the developed theory of matched spaces of time scales, the basic theory of dynamic equations under matched space of time scales is established and some effective methods are provided to study the almost periodic solutions of dynamic equations on hybrid time scales.