Pseudo almost automorphic mild solutions to non-autonomous differential equations in the “strong topology”

This paper established some results on the existence of pseudo almost automorphic mild solutions to non-autonomous linear and semi-linear differential equations using exponential dichotomy of the evolution family and Bi-pseudo almost automorphy of Green’s function in the “strong topology”. In our results, the assumption for Green’s function “Bi-almost automorphic” is weaken as “Bi-pseudo almost automorphic” in the “strong topology”. Moreover, we consider the semi-linear differential equations under some compact conditions instead of Lipschitz conditions.