Pseudo almost periodic solutions to some differential equations

This paper is concerned with the pseudo almost periodic solutions to the abstract differential equations of the form:ddsw(s)=Aw(s)+Bw(s)+f(s)(*),where A,B are densely defined closed linear operators acting in a Hilbert space H, and f:R↦H is a H-valued pseudo almost periodic function. Using the theory of the invariant subspaces for unbounded linear operators, we show that every bounded solution to (*) is a pseudo almost periodic function.