Pseudo asymptotically periodic mild solutions of semilinear functional integro‐differential equations in Banach spaces. (10th August 2017)

• Record Type: Journal Article
• Authors: Xia, Zhinan; Wang, Dingjiang; Wen, Ching‐Feng; Yao, Jen‐Chih
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 18(2018)
• Page Start: 7333
• Page End: 7355
• Publication Date: 2017-08-10
• Subjects: exponential dichotomy -- Hille‐Yosida operators -- integro‐differential equations -- mild solutions -- (μ, ν)‐pseudo S‐asymptotic ω‐periodicity; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4533
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we introduce and investigate the functions of ( μ, ν )‐pseudo S ‐asymptotically ω ‐periodic of class r (class infinity). We systematically explore the properties of these functions in Banach space including composition theorems. As applications, we establish some sufficient criteria for ( μ, ν )‐pseudo S ‐asymptotic ω ‐periodicity of (nonautonomous) semilinear integro‐differential equations with finite or infinite delay. Finally, some interesting examples are presented to illustrate the main findings.