{"title":"On neutral integrodifferential equations with state-dependent delay in Banach spaces","authors":"Mbarack Fall, Aziz Mané, Ramkumar Kasinathan, Ravikumar Kasinathan, Mamadou Abdoul Diop","doi":"10.1007/s13370-024-01193-6","DOIUrl":null,"url":null,"abstract":"<div><p>In this work, we investigate the existence of mild solution for semilinear integro-differential systems and semilinear neutral integro-differential systems with state-dependent delay in Banach spaces. Using Mönch’s fixed point theorem, the theory of Grimmer’s resolvent operator and the idea of measures of non-compactness, we prove the existence results. At the end, an example is given to further illustrate the conclusions drawn from the theoretical study.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 2","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-024-01193-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this work, we investigate the existence of mild solution for semilinear integro-differential systems and semilinear neutral integro-differential systems with state-dependent delay in Banach spaces. Using Mönch’s fixed point theorem, the theory of Grimmer’s resolvent operator and the idea of measures of non-compactness, we prove the existence results. At the end, an example is given to further illustrate the conclusions drawn from the theoretical study.