{"title":"Periodic solution for neutral-type differential equation with piecewise impulses on time scales","authors":"Chun Peng, Xiaoliang Li, Bo Du","doi":"10.1186/s13661-024-01916-5","DOIUrl":null,"url":null,"abstract":"In this paper, we establish the existence and stability of periodic solutions for neutral-type differential equations with piecewise impulses on time scales. We first obtain some sufficient conditions for the existence of a unique periodic solution by using the Banach contraction mapping principle. We also prove the existence of at least one periodic solution using the Schauder fixed point theorem. In addition, we establish the stability results based on the existence of periodic solutions. It is worth noting that the results of this paper are based on time scales, so that they are applicable to continuous, discrete, and other types of systems.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"2 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Boundary Value Problems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13661-024-01916-5","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: 0
Abstract
In this paper, we establish the existence and stability of periodic solutions for neutral-type differential equations with piecewise impulses on time scales. We first obtain some sufficient conditions for the existence of a unique periodic solution by using the Banach contraction mapping principle. We also prove the existence of at least one periodic solution using the Schauder fixed point theorem. In addition, we establish the stability results based on the existence of periodic solutions. It is worth noting that the results of this paper are based on time scales, so that they are applicable to continuous, discrete, and other types of systems.
期刊介绍:
The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.