{"title":"Differentiability of Semi-Flow for Impulsive Evolution Equation with State-Dependent Delay","authors":"Weifeng Ma, Yongxiang Li","doi":"10.1007/s12346-024-01134-5","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we study the impulsive evolution equation with state-dependent delay by the theory of operator semigroup in Banach spaces. Under conditions that both nonlinearity and impulsive functions are Lipschitz continuous, we obtain the existence and uniqueness results of mild solution. Furthermore, we prove the differentiability of a semi-flow defined by a continuously differentiable solution operator under the appropriate condition.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Qualitative Theory of Dynamical Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12346-024-01134-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the impulsive evolution equation with state-dependent delay by the theory of operator semigroup in Banach spaces. Under conditions that both nonlinearity and impulsive functions are Lipschitz continuous, we obtain the existence and uniqueness results of mild solution. Furthermore, we prove the differentiability of a semi-flow defined by a continuously differentiable solution operator under the appropriate condition.
期刊介绍：
Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.
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