{"title":"不确定均质线性系统的利乌维尔公式和系统的显式解。","authors":"Vahid Roomi, Hamid Reza Ahmadi","doi":"10.1007/s12591-021-00573-9","DOIUrl":null,"url":null,"abstract":"<p><p>This paper presents some new definitions and results about a system of uncertain homogeneous linear differential equations. Introducing the uncertain fundamental system and uncertain fundamental matrix for the uncertain system, the Liouville formula will be proven for the system. Moreover, the explicit solutions of the system will be presented.</p>","PeriodicalId":45352,"journal":{"name":"Differential Equations and Dynamical Systems","volume":" ","pages":"1-14"},"PeriodicalIF":0.8000,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8200317/pdf/","citationCount":"0","resultStr":"{\"title\":\"The Liouville Formula for the Uncertain Homogeneous Linear System and Explicit Solutions of the System.\",\"authors\":\"Vahid Roomi, Hamid Reza Ahmadi\",\"doi\":\"10.1007/s12591-021-00573-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>This paper presents some new definitions and results about a system of uncertain homogeneous linear differential equations. Introducing the uncertain fundamental system and uncertain fundamental matrix for the uncertain system, the Liouville formula will be proven for the system. Moreover, the explicit solutions of the system will be presented.</p>\",\"PeriodicalId\":45352,\"journal\":{\"name\":\"Differential Equations and Dynamical Systems\",\"volume\":\" \",\"pages\":\"1-14\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-06-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8200317/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations and Dynamical Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s12591-021-00573-9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations and Dynamical Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12591-021-00573-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
The Liouville Formula for the Uncertain Homogeneous Linear System and Explicit Solutions of the System.
This paper presents some new definitions and results about a system of uncertain homogeneous linear differential equations. Introducing the uncertain fundamental system and uncertain fundamental matrix for the uncertain system, the Liouville formula will be proven for the system. Moreover, the explicit solutions of the system will be presented.
期刊介绍：
Aims and Scope Differential Equations and Dynamical Systems is a multidisciplinary journal whose aim is to publish high quality original research papers in Ordinary and Partial Differential Equations, Integral and Integro-Differential Equations, Calculus of Variations, Bifurcation Theory and Dynamical Systems Theory. Articles devoted to the application of methods and techniques from the above fields of Analysis to Neural Networks, Control Theory; Physical, Biological, Medical, Social and Engineering Sciences are also welcome.In particular, for studies related to modelling aspects in all the above areas, it is essential that the mathematical results be interpreted and translated to the application domains by substantiating the usefulness of the research in solving problems in those realms. Papers dealing with computational and numerical aspects will not be considered for publication unless supported by strong theoretical results and analyses. MissionThe mission of the journal envisages to serve scientists through prompt publication of significant advances in the branches of science and technology beforehand outlined and to provide a forum for the discussion of new scientific developments.
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