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https://doi.org/10.11948/20200072

has been cited by the following article:

• TITLE: Existence of Solutions for a Non-Autonomous Evolution Equations with Nonlocal Conditions

  AUTHORS: Lixin Sheng, Weimin Hu, Youhui Su, Yongzhen Yun

  KEYWORDS: Non-Autonomous Evolution Equation, Nonlocal Conditions, Mild Solution, Evolution Family

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.12, December 29, 2023

  ABSTRACT: The existence of mild solutions for non-autonomous evolution equations with nonlocal conditions in Banach space is studied in this article. We obtained the existence of at least one mild solution to the evolution equations by using Krasnoselskii’s fixed point theorem as well as the theory of the evolution family. The interest of this paper is that any assumptions are not imposed on the nonlocal terms and Green’s functions and a new alternative method is applied to prove the existence of mild solutions. The results obtained in this paper may improve some related conclusions on this topic. An example is given as an application of the results.