{"title":"Multiple Solutions for Lie´nard Type Generalized Equations","authors":"A. Kirichuka, F. Sadyrbaev","doi":"10.37394/23202.2023.22.58","DOIUrl":null,"url":null,"abstract":"Two-point boundary value problems for second-order ordinary differential equations of Lie´nard type are studied. A comparison is made between equations x´´ + f (x) x´2 + g(x) = 0 and x´´ + f (x) x´ + g(x) = 0. In our approach, the Dirichlet boundary conditions are considered. The estimates of the number of solutions in both cases are obtained. These estimates are based on considering the equation of variations around the trivial solution and some additional assumptions. Examples and visualizations are supplied.","PeriodicalId":39422,"journal":{"name":"WSEAS Transactions on Systems and Control","volume":"69 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"WSEAS Transactions on Systems and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/23202.2023.22.58","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
Two-point boundary value problems for second-order ordinary differential equations of Lie´nard type are studied. A comparison is made between equations x´´ + f (x) x´2 + g(x) = 0 and x´´ + f (x) x´ + g(x) = 0. In our approach, the Dirichlet boundary conditions are considered. The estimates of the number of solutions in both cases are obtained. These estimates are based on considering the equation of variations around the trivial solution and some additional assumptions. Examples and visualizations are supplied.
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WSEAS Transactions on Systems and Control publishes original research papers relating to systems theory and automatic control. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with systems theory, dynamical systems, linear and non-linear control, intelligent control, robotics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.
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