Existence and uniqueness of pseudo-almost periodic solutions to some classes of semilinear differential equations and applications

This paper is concerned with the existence and uniqueness of pseudo-almost periodic solutions to the class of semilinear differential equations of the formu′(t)+Au(t)=f(t,Bu(t)),(*),where -A-A is the infinitesimal generator of an analytic semigroup acting on a (complex) Banach space XX, B:D(B)⊂X↦XB:D(B)⊂X↦X is a densely defined closed linear operator, and f:R×X↦Xf:R×X↦X is a jointly continuous function. Under some suitable assumptions on A,BA,B, and f  , the existence and uniqueness of a pseudo-almost periodic solution to (*)(*) is obtained.