Behavior of bounded solutions for some almost periodic neutral partial functional differential equations. (26th August 2016)

• Record Type: Journal Article
• Authors: Ait Dads, El Hadi; Es‐sebbar, Brahim; Ezzinbi, Khalil; Ziat, Mohamed
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 7(2017)
• Page Start: 2377
• Page End: 2397
• Publication Date: 2016-08-26
• Subjects: Stepanov almost periodic functions -- bounded solutions -- almost periodic solutions -- semigroup -- neutral functional differential equations; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4145
• Languages: English
• ISSNs: 0170-4214

Abstract

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 R are almost periodic. Copyright © 2016 John Wiley & Sons, Ltd.