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

Yu, Fei

doi:10.3390/math10030435

Cited by 2 publications

(1 citation statement)

References 12 publications

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“…For further information about Besicovitch almost periodic functions, Besicovitch almost automorphic functions and their applications, we refer the reader to [1,2,4,5,6,7,9,11,12], [13,14,15,16,29,31,32,35], [36,49,51,53,54,56,57,58,60] and references cited therein; we would like to specially emphasize here the important research monograph [55] by A. A. Pankov.…”

Section: Introductionmentioning

confidence: 99%

Multi-dimensional Besicovitch almost periodic type functions and applications

Kostić¹

2022

Preprint

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In this paper, we analyze multi-dimensional Besicovitch almost periodic type functions. We clarify the main structural properties for the introduced classes of Besicovitch almost periodic type functions, explore the notion of Besicovitch-Doss almost periodicity in the multi-dimensional setting, and provide some applications of our results to the abstract Volterra integrodifferential equations and the partial differential equations.

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Section: Introductionmentioning

confidence: 99%

Multi-dimensional Besicovitch almost periodic type functions and applications

Kostić¹

2022

Preprint

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Besicovitch almost automorphic solutions in finite‐dimensional distributions to stochastic semilinear differential equations driven by both Brownian and fractional Brownian motions

Li,

Bai

2024

Math Methods in App Sciences

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In this paper, we are concerned with a stochastic semilinear differential equations driven by both Brownian motion and fractional Brownian motion. Firstly, we establish an inequality for the distance between finite‐dimensional distributions of a random process at two different moments. Then, using the properties of stochastic integrals, fixed point theorems, and based on this inequality, we establish the existence and uniqueness of Besicovich almost automorphic solutions in finite‐dimensional distributions for this type of semilinear equation. Finally, we provide an example to demonstrate the effectiveness of our results. Our results are new to stochastic differential equations driven by Brownian motion or stochastic differential equations driven by fractional Brownian motion.

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

Cited by 2 publications

References 12 publications

Multi-dimensional Besicovitch almost periodic type functions and applications

Multi-dimensional Besicovitch almost periodic type functions and applications

Besicovitch almost automorphic solutions in finite‐dimensional distributions to stochastic semilinear differential equations driven by both Brownian and fractional Brownian motions

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