{"title":"具有卷积基尔霍夫函数的非局部椭圆方程的精确解和分岔曲线","authors":"Tetsutaro Shibata","doi":"10.1186/s13661-024-01871-1","DOIUrl":null,"url":null,"abstract":"We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with convolutional Kirchhoff functions. We establish the exact solutions $u_{\\lambda}$ and bifurcation curves $\\lambda (\\alpha )$ , where $\\alpha := \\Vert u_{\\lambda}\\Vert _{\\infty}$ .","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exact solutions and bifurcation curves of nonlocal elliptic equations with convolutional Kirchhoff functions\",\"authors\":\"Tetsutaro Shibata\",\"doi\":\"10.1186/s13661-024-01871-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with convolutional Kirchhoff functions. We establish the exact solutions $u_{\\\\lambda}$ and bifurcation curves $\\\\lambda (\\\\alpha )$ , where $\\\\alpha := \\\\Vert u_{\\\\lambda}\\\\Vert _{\\\\infty}$ .\",\"PeriodicalId\":49228,\"journal\":{\"name\":\"Boundary Value Problems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-05-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Boundary Value Problems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1186/s13661-024-01871-1\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Boundary Value Problems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13661-024-01871-1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Exact solutions and bifurcation curves of nonlocal elliptic equations with convolutional Kirchhoff functions
We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with convolutional Kirchhoff functions. We establish the exact solutions $u_{\lambda}$ and bifurcation curves $\lambda (\alpha )$ , where $\alpha := \Vert u_{\lambda}\Vert _{\infty}$ .
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The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.
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