Pseudo S-Asymptotically Periodic Solutions of Second-Order Abstract Cauchy Problems

In this work we discuss the existence of pseudo S-asymptotically periodic mild solutions for a second order abstract Cauchy problem. In particular, we show that pseudo S-asymptotically ω-periodic cosine functions of operators are ω-periodic. The paper is completed with an application to the nonautonomous wave equation. © 2015 Elsevier Inc.