-order -almost periodic functions and dynamic equations. Issue 15 (18th November 2018)

• Record Type: Journal Article
• Authors: Wang, Chao; Agarwal, Ravi P.; O'Regan, Donal
• Is Part Of: Applicable analysis. Volume 97:Issue 15(2018)
• Page Start: 2626
• Page End: 2654
• Publication Date: 2018-11-18
• Subjects: Time scales -- almost periodic functions -- matched spaces -- delay dynamic equations; 26E70 -- 33E30 -- 34N05 -- 34C27; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1382689
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract: In this paper, using matched spaces for time scales, we introduce new types of almost periodic functions, including -almost periodic functions and -order -almost periodic functions ( -almost periodic functions). Also we introduce the definition of hull equations for homogeneous dynamic equations and obtain some existence results. Under exponential dichotomy for the corresponding homogeneous equation, we obtain the form of a -almost periodic solution with the -almost periodic affiliated function for a type of nonhomogeneous dynamic equation and we use it to study the existence of -almost periodic solutions with the -almost periodic affiliated function for new delay dynamic equations.