On the Stepanov almost periodic solution of a second-order infinitesimal generator differential equation (Q1187081)

The existence of an almost periodic solution of the problem \(u''(t)=Au'(t)+Bu(t)+f(t)\) a.e. \(t\in J\), on \(X\) is investigated, where \(X\) is a Banach space, \(A\) is the infinitesimal generator of an almost periodic group. \(B\) is a densely-defined closed linear operator and \(f\) is an almost periodic (in the sense of Stepanov) continuous function.