{"title":"On a Piecewise Constant Control for Nonlinear Differential Equations in a Banach Space","authors":"A. A. Sedipkov","doi":"10.1134/s105513442402007x","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the problem on controlling solutions of nonlinear differential equations with\nunstable equilibrium states. We assume that the operator of the linearized problem is bounded\nand its spectrum is located in the right half-plane. We prove that there exists a control such that\nthe solution remains in a prescribed neighborhood of an equilibrium state as long as required.\n</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Advances in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s105513442402007x","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
We study the problem on controlling solutions of nonlinear differential equations with
unstable equilibrium states. We assume that the operator of the linearized problem is bounded
and its spectrum is located in the right half-plane. We prove that there exists a control such that
the solution remains in a prescribed neighborhood of an equilibrium state as long as required.
期刊介绍：
Siberian Advances in Mathematics is a journal that publishes articles on fundamental and applied mathematics. It covers a broad spectrum of subjects: algebra and logic, real and complex analysis, functional analysis, differential equations, mathematical physics, geometry and topology, probability and mathematical statistics, mathematical cybernetics, mathematical economics, mathematical problems of geophysics and tomography, numerical methods, and optimization theory.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
