On the stepanov almost periodic solution of a second‐order infinitesimal generator differential equation

Almost Periodic Functions and Their Applications: A Survey of Results and Perspectives

“…For the periodic solutions of abstract first-order differential equations, we refer the reader to the research monographs [21] by Burton,[22] by Liu, Guerekata, and Minh, and [23] by Yoshizawa. e notion of almost periodic cosine operator functions was introduced by Cioranescu [24] and after that received considerable attention of many authors. e existence and uniqueness of almost periodic-type solutions of the (abstract) second-order differential equations have been investigated in many research articles by now, using the theory of cosine operator functions or other methods (see, e.g., [25][26][27][28][29][30][31][32][33]). For example, Diagana, Hassan, and Messaoudi recently analyzed, in [34], the existence of asymptotically almost periodic mild solutions of the abstract Volterra integrodifferential equation…”