{"title":"Total controllability of nonlocal semilinear functional evolution equations with non-instantaneous impulses","authors":"J. Kumar, S. Singh, S. Arora, J. Dabas","doi":"10.1007/s13226-024-00613-4","DOIUrl":null,"url":null,"abstract":"<p>In this article, we are discussing a more vital concept of controllability, termed total controllability. We have considered a nonlocal semilinear functional evolution equation with non-instantaneous impulses and finite delay in Hilbert spaces. A set of sufficient conditions of total controllability is obtained for the evolution system under consideration by imposing the theory of <span>\\(C_0\\)</span>-semigroup and Banach fixed point theorem. We also established the total controllability results for a functional integro-differential equation. Finally, an example demonstrates the feasibility of derived abstract results.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"13 50 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13226-024-00613-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we are discussing a more vital concept of controllability, termed total controllability. We have considered a nonlocal semilinear functional evolution equation with non-instantaneous impulses and finite delay in Hilbert spaces. A set of sufficient conditions of total controllability is obtained for the evolution system under consideration by imposing the theory of \(C_0\)-semigroup and Banach fixed point theorem. We also established the total controllability results for a functional integro-differential equation. Finally, an example demonstrates the feasibility of derived abstract results.
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