Almost Automorphic and Pseudo-Almost Automorphic Solutions to Semilinear Evolution Equations with Nondense Domain

In recent years, the theory of almost automorphic functions has been developed extensively see, e.g., Bugajewski and N’guérékata 1 , Cuevas and Lizama 2 , and N’guérékata 3 and the references therein . However, literature concerning pseudo-almost automorphic functions is very new cf. 4 . It is well known that the study of composition of two functions with special properties is important and basic for deep investigations. Recently an interesting article has appeared by Liang et al. 5 concerning the composition of pseudoalmost automorphic functions. The same authors in 6 have applied the results to obtain pseudo-almost automorphic solutions to semilinear differentail equations see also 7 . On the other hand, in article by Blot et al. 8 , the authors have obtained existence and uniqueness of pseudo-almost automorphic solutions to some classes of partial evolutions equations. In this work, we study the existence and uniqueness of almost automorphic and pseudo-almost automorphic solutions for a class of abstract differential equations described in the form