Abstract
In this paper, we first put forward a concept of Besicovitch almost periodic functions on time scales defined by Bochner property, and study some fundamental properties of this kind of Besicovitch almost periodic functions, including the closeness to linear operations, translation invariance, composition theorem, etc. Then, as an application of our results, the existence and uniqueness of Besicovitch almost periodic solutions for a class of nonautonomous semilinear evolution dynamic equation with varying delay on time scales are established.
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This work is supported by the National Natural Science Foundation of China under Grant Nos. 12261098, 11861072 and the Applied Basic Research Foundation of Yunnan Province under Grant No. 2019FB003.
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Li, Y., Qi, W. & Li, B. Besicovitch Almost Periodic Solutions to Semilinear Evolution Dynamic Equations with Varying Delay. Qual. Theory Dyn. Syst. 22, 29 (2023). https://doi.org/10.1007/s12346-022-00735-2
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DOI: https://doi.org/10.1007/s12346-022-00735-2