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Existence and Approximate Controllability of Solutions for an Impulsive Evolution Equation with Nonlocal Conditions in Banach Space
  
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KeyWord:Impulsive evolution equation, approximate controllability, nonlocal conditions, resolvent operator, evolution family
Author NameAffiliation
Lixin Sheng School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, Jiangsu, China
School of Mathematics and Statistics, Yili Normal University, Yining, Xinjiang, China 
Weimin Hu School of Mathematics and Statistics, Yili Normal University, Yining, Xinjiang, China
Institute of Applied Mathematics, Yili Normal University, Yining, Xinjiang, China 
You-Hui Su School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, Jiangsu, China 
Yongzhen Yun School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, Jiangsu, China 
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Abstract:
      In this article, we study the existence of mild solutions and approximate controllability for non-autonomous impulsive evolution equations with nonlocal conditions in Banach space. The existence of mild solutions and some conditions for approximate controllability of these non-autonomous impulsive evolution equations are given by using the Krasnoselskii's fixed point theorem, the theory of evolution family and the resolvent operator. In particular,the impulsive functions are supposed to be continuous and the nonlocal item is divided into Lipschitz continuous and completely bounded. An example is given as an application of the results.