n 0 -Order Weighted Pseudo ?-Almost Automorphic Functions and Abstract Dynamic Equations

Chao Wang, Ravi P. Agarwal, Donal O’Regan and Gaston M. N’Guérékata
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Chao Wang: Department of Mathematics, Yunnan University, Kunming 650091, China
Ravi P. Agarwal: Distinguished University Professor of Mathematics, Florida Institute of Technology, 150 West University Boulevard, Melbourne, FL 32901, USA
Donal O’Regan: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
Gaston M. N’Guérékata: Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA

Mathematics, 2019, vol. 7, issue 9, 1-25

Abstract: In this paper, we introduce the concept of a n 0 -order weighted pseudo Δ n 0 δ -almost automorphic function under the matched space for time scales and we present some properties. The results are valid for q -difference dynamic equations among others. Moreover, we obtain some sufficient conditions for the existence of weighted pseudo Δ n 0 δ -almost automorphic mild solutions to a class of semilinear dynamic equations under the matched space. Finally, we end the paper with a further discussion and some open problems of this topic.

Keywords: time scales; seighted pseudo ? n 0 ? -almost automorphic functions; abstract dynamic equations; mild solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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