Weyl almost periodic solutions to abstract linear and semilinear equations with Weyl almost periodic coefficients

Abstract

In this work, we study the existence and uniqueness of bounded Weyl almost periodic solution to the abstract differential equation u ' (t) = Au(t) + f (t), t $\in$ R, in a Banach space X, where A : D (A) $\subset$ X $\rightarrow$ X is a linear operator (unbounded) which generates an exponentially stable C 0-semigroup on X and f : R $\rightarrow$ X is a Weyl almost periodic function. We also investigate the nonautonomous case.