Almost Automorphic Solutions in the Sense of Besicovitch to Nonautonomous Semilinear Evolution Equations

Yu Fei and Yongkun Li
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Yu Fei: School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
Yongkun Li: Department of Mathematics, Yunnan University, Kunming 650091, China

Mathematics, 2022, vol. 10, issue 3, 1-15

Abstract: In this paper, we study the existence of almost automorphic solutions in the sense of Besicovitch for a class of semilinear evolution equations. Firstly, we study some basic properties of almost automorphic functions in the sense of Besicovitch, including the composition theorem. Then, by using the Banach fixed point theorem, the existence of almost automorphic solutions in the sense of Besicovitch to the semilinear equation is obtained. Finally, we give an example of partial differential equations to illustrate the applicability of our results.

Keywords: nonautonomous semilinear evolution equation; almost automorphic solution in the sense of Besicovitch; fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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