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

作　　者：Lixin Sheng Weimin Hu Youhui Su Yongzhen Yun Lixin Sheng;Weimin Hu;Youhui Su;Yongzhen Yun(School of Mathematics and Statistics, Yili Normal University, Yining, China;School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, China;Institute of Applied Mathematics, Yili Normal University, Yining, China)

机构地区：[1]School of Mathematics and Statistics, Yili Normal University, Yining, China [2]School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, China [3]Institute of Applied Mathematics, Yili Normal University, Yining, China

出　　处：《Journal of Applied Mathematics and Physics》2023年第12期4079-4091,共13页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：Non-Autonomous Evolution Equation Nonlocal Conditions Mild Solution Evolution Family 

分 类 号：O17[理学—数学]