Advances in Mathematical Physics (Jan 2021)

Asymptotic Behavior of Solution for Functional Evolution Equations with Stepanov Forcing Terms

  • Zhong-Hua Wu

DOI
https://doi.org/10.1155/2021/4412527
Journal volume & issue
Vol. 2021

Abstract

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Through the use of the measure theory, evolution family, “Acquistapace–Terreni” condition, and Hölder inequality, the core objective of this work is to seek to analyze whether there is unique μ-pseudo almost periodic solution to a functional evolution equation with Stepanov forcing terms in a Banach space. Certain adequate conditions are derived guaranteeing there is unique μ-pseudo almost periodic solution to the equation by Lipschitz condition and contraction mapping principle. Finally, an example is used to demonstrate our theoretical findings.