{"title":"Lie ' nard型广义方程的多重解","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":"{\"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}","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
摘要
研究了一类二阶Lie ' nard型常微分方程的两点边值问题。比较了方程x′′+ f (x) x′2 + g(x) = 0和方程x′′+ f (x) x′+ g(x) = 0。在我们的方法中，考虑了狄利克雷边界条件。得到了两种情况下解的估计数目。这些估计是基于考虑围绕平凡解的变化方程和一些额外的假设。提供了示例和可视化。
Multiple Solutions for Lie´nard Type Generalized Equations
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.
期刊介绍：
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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