{"title":"封闭流形上奇异基尔霍夫型方程的存在性和唯一性结果","authors":"Mohamed El Farouk Ounane , Kamel Tahri","doi":"10.1016/j.difgeo.2023.102094","DOIUrl":null,"url":null,"abstract":"<div><p><span><span><span>Using the variational methods and the </span>critical points theory, we prove the existence and the uniqueness of a positive solution for a singular </span>Kirchhoff<span> type equation on a closed Riemannian manifold of dimension </span></span><span><math><mi>N</mi><mo>≥</mo><mn>3</mn></math></span>. At the end, we give a geometric application involving the conformal Laplacian.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"93 ","pages":"Article 102094"},"PeriodicalIF":0.6000,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence and uniqueness results for a singular Kirchhoff type equation on a closed manifold\",\"authors\":\"Mohamed El Farouk Ounane , Kamel Tahri\",\"doi\":\"10.1016/j.difgeo.2023.102094\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span><span><span>Using the variational methods and the </span>critical points theory, we prove the existence and the uniqueness of a positive solution for a singular </span>Kirchhoff<span> type equation on a closed Riemannian manifold of dimension </span></span><span><math><mi>N</mi><mo>≥</mo><mn>3</mn></math></span>. At the end, we give a geometric application involving the conformal Laplacian.</p></div>\",\"PeriodicalId\":51010,\"journal\":{\"name\":\"Differential Geometry and its Applications\",\"volume\":\"93 \",\"pages\":\"Article 102094\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Geometry and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0926224523001201\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224523001201","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Existence and uniqueness results for a singular Kirchhoff type equation on a closed manifold
Using the variational methods and the critical points theory, we prove the existence and the uniqueness of a positive solution for a singular Kirchhoff type equation on a closed Riemannian manifold of dimension . At the end, we give a geometric application involving the conformal Laplacian.
期刊介绍：
Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.
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