\(C\)-semigroups and almost periodic solutions of evolution equations (Q1883432)

The paper is concerned with the existence of almost periodic mild solutions to the abstract differential equation \[ u'(t)=Au(t)+f(t) \] on a Banach space \(X\), where \(A\) generates a \(C\)-semigroup and \(f\) is an almost periodic function. Using the evolution \(C\)-semigroup associated with the \(C\)-semigroup generated by \(A\) as the main tool, the authors extend the known results on the existence of almost periodic solutions to the above equation, when \(A\) generates a \(C_0\)-semigroup, to a more general class of operators.