Behavior of bounded solutions for some almost periodic neutral partial functional differential equations

Abstract

We establish a Bochner type characterization for Stepanov almost periodic functions, and we prove a new result about the integration of almost periodic functions. This result is then used together with a reduction principle to investigate the nature of bounded solutions of some almost periodic partial neutral functional differential equations. More specifically, we prove that all bounded solutions on double-struckR are almost periodic. Copyright © 2016 John Wiley & Sons, Ltd.

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

“…We can mention, in the deterministic case, the works by Andres and Pennequin, Long and Ding, Ding et al Hu and Mingarelli, Henriquez, Rao, and Zaidman . Particularly, Long and Ding, Ding et al and Ait Dads et al show the existence and uniqueness of almost periodic solution for an abstract semilinear evolution equation with Stepanov almost periodic coefficients. They prove the existence and uniqueness of a Bohr almost periodic mild solution.…”