S -Almost Automorphic Solutions for Impulsive Evolution Equations on Time Scales in Shift Operators

Chao Wang, Rathinasamy Sakthivel and Gaston M. N’Guérékata
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Chao Wang: Department of Mathematics, Yunnan University, Kunming 650091, Yunnan, China
Rathinasamy Sakthivel: Department of Applied Mathematics, Bharathiar University, Coimbatore, Tamil Nadu 641046, India
Gaston M. N’Guérékata: Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA

Mathematics, 2020, vol. 8, issue 6, 1-28

Abstract: In this paper, based on the concept of complete-closed time scales attached with shift direction under non-translational shifts (or S -CCTS for short), as a first attempt, we develop the concepts of S -equipotentially almost automorphic sequences, discontinuous S-almost automorphic functions and weighted piecewise pseudo S -almost automorphic functions. More precisely, some novel results about their basic properties and some related theorems are obtained. Then, we apply the introduced new concepts to investigate the existence of weighted piecewise pseudo S -almost automorphic mild solutions for the impulsive evolution equations on irregular hybrid domains. The obtained results are valid for q -difference partial dynamic equations and can also be extended to other dynamic equations on more general time scales. Finally, some heat dynamic equations on various hybrid domains are provided as applications to illustrate the obtained theory.

Keywords: S -almost automorphic functions; impulsive evolution equations; mild solutions; time scales (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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