(untitled) (Nonlinear Studies, 2012)
We deal in this paper with ρ-pseudo almost periodic and ρ-pseudo almost automorphic mild solutions to the semilinear integro-differential equation u’(t)=Au(t)+_-∞^ta(t-s)Au(s)ds+f(t,Bu(t)). t, where A generates a uniformly integrable semigroup of operators in a Banach space X, and BL(X). We give an example of non uniqueness of the decomposition of ρ-pseudo almost automorphic functions. We also discuss some properties of weakly almost automorphic functions. These results extend and complement some recent ones on this topic.