Almost automorphic dynamic equations on translation time scales

This chapter is mainly concerned with almost automorphic and generalized solutions for dynamic equations of different types on translation time scales and the chapter is divided into four sections. In Sect. 8.1, the existence of weighted pseudo almost automorphic solutions of abstract dynamic equations in Banach space is considered. In Sect. 8.2, we study a type of abstract impulsive ∇-dynamic equations and obtain some sufficient conditions on the existence and exponential stability of weighted piecewise pseudo almost automorphic mild solutions. In Sect. 8.3, a class of semilinear dynamic equations on changing-periodic time scales is proposed and investigated, and existence conditions of local pseudo almost automorphic mild solutions are presented. In Sect. 8.4, the almost automorphy of solutions on semigroups induced by time scales to dynamic equations is studied and some related results are established.