Pseudo almost periodic solutions to some differential equations Original Research Article

This paper is concerned with the pseudo almost periodic solutions to the abstract differential equations of the form: View the MathML sourceddsw(s)=Aw(s)+Bw(s)+f(s)(*), Turn MathJax on where A,BA,B are densely defined closed linear operators acting in a Hilbert space HH, and View the MathML sourcef:R↦H is a HH-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.