Weighted Pseudo Almost-Periodic Functions and Applications to Semilinear Evolution Equations

We first give a solution to a key problem concerning the completeness of the space of weighted pseudo almost-periodic functions and then establish a new composition theorem with respect to these functions. Some important remarks with concrete examples are also presented. Moreover, we prove an existence theorem for the weighted pseudo almost-periodic mild solution to the semilinear evolution equation:x′(t)=Ax(t)+f(t,x(t)),t∈ℝ, whereAis the infinitesimal generator of an exponentially stableC0-semigroup. An application is also given to illustrate the abstract existence theorem.