{"title":"ON DISCRETE SYSTEMS WITH POTENTIAL OPERATORS","authors":"V. Savchin, P. Trinh","doi":"10.18287/2541-7525-2021-27-3-74-82","DOIUrl":null,"url":null,"abstract":"The main purpose of this work is to study the potentiality of a discrete system obtained from the system of the form C(t, u)u_ (t)+E(t, u) = 0 with continuous time. The definition of potentiality of the corresponding discrete system is introduced. Necessary and sufficient conditions for its potentiality with respect to a given bilinear form are obtained. The algorithm for the construction of the corresponding functionalthe analogue of the Hamiltonian actionis presented. The illustrative example is given.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"60 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik of Samara University. Natural Science Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18287/2541-7525-2021-27-3-74-82","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
The main purpose of this work is to study the potentiality of a discrete system obtained from the system of the form C(t, u)u_ (t)+E(t, u) = 0 with continuous time. The definition of potentiality of the corresponding discrete system is introduced. Necessary and sufficient conditions for its potentiality with respect to a given bilinear form are obtained. The algorithm for the construction of the corresponding functionalthe analogue of the Hamiltonian actionis presented. The illustrative example is given.
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