Pseudo almost automorphic solutions to semilinear differential equations

In this paper we study the semilinear differential equation x´(t) = Ax(t) + f(t, x(t)),t ∈ R in Banach spaces, where A is a (an) bounded (unbounded) linear operator. Applying the theory of dissipative operator, the theory of C₀-semigroups and Banach contraction principle, we establish the existence and uniqueness of a bounded pseudo almost automorphic solution of the problem under conditions.