Sebastián Lalvay, Adrian Padilla-segarra, W. Zouhair
{"title":"On the existence and uniqueness of solutions for non-autonomous semi-linear systems with non-instantaneous impulses, delay, and non-local conditions","authors":"Sebastián Lalvay, Adrian Padilla-segarra, W. Zouhair","doi":"10.18514/mmn.2022.3785","DOIUrl":null,"url":null,"abstract":"A non-autonomous evolution semi-linear differential system under non-instantaneous impulses, delays, and perturbed by non-local conditions is studied. Its piece-wise continuous solutions belong to a finite dimensional Banach space. The existence and uniqueness of solutions on the interval [−r,τ] are obtained by applying Karakostas’ fixed-point theorem. Further results concerning solution prolongation are developed. An example is presented, and several remarks on the infinite-dimensional case are included. 2010 Mathematics Subject Classification: 93C10; 93C23","PeriodicalId":49806,"journal":{"name":"Miskolc Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2022-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Miskolc Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.18514/mmn.2022.3785","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 5
Abstract
A non-autonomous evolution semi-linear differential system under non-instantaneous impulses, delays, and perturbed by non-local conditions is studied. Its piece-wise continuous solutions belong to a finite dimensional Banach space. The existence and uniqueness of solutions on the interval [−r,τ] are obtained by applying Karakostas’ fixed-point theorem. Further results concerning solution prolongation are developed. An example is presented, and several remarks on the infinite-dimensional case are included. 2010 Mathematics Subject Classification: 93C10; 93C23
期刊介绍：
Miskolc Mathematical Notes, HU ISSN 1787-2405 (printed version), HU ISSN 1787-2413 (electronic version), is a peer-reviewed international mathematical journal aiming at the dissemination of results in many fields of pure and applied mathematics.
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