{"title":"$\\mathbb{S}^{2}$上平均场方程的多重轴对称解","authors":"Zhuoran Du","doi":"10.4208/ata.oa-0016","DOIUrl":null,"url":null,"abstract":"We study the following mean field equation ∆gu + ρ ( eu ∫ S2 e udμ − 1 4π ) = 0 in S2, where ρ is a real parameter. We obtain the existence of multiple axially asymmetric solutions bifurcating from u = 0 at the values ρ = 4n(n + 1)π for any odd integer n ≥ 3.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"23 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Multiple Axially Asymmetric Solutions to a Mean Field Equation on $\\\\mathbb{S}^{2}$\",\"authors\":\"Zhuoran Du\",\"doi\":\"10.4208/ata.oa-0016\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the following mean field equation ∆gu + ρ ( eu ∫ S2 e udμ − 1 4π ) = 0 in S2, where ρ is a real parameter. We obtain the existence of multiple axially asymmetric solutions bifurcating from u = 0 at the values ρ = 4n(n + 1)π for any odd integer n ≥ 3.\",\"PeriodicalId\":29763,\"journal\":{\"name\":\"Analysis in Theory and Applications\",\"volume\":\"23 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis in Theory and Applications\",\"FirstCategoryId\":\"95\",\"ListUrlMain\":\"https://doi.org/10.4208/ata.oa-0016\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis in Theory and Applications","FirstCategoryId":"95","ListUrlMain":"https://doi.org/10.4208/ata.oa-0016","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Multiple Axially Asymmetric Solutions to a Mean Field Equation on $\mathbb{S}^{2}$
We study the following mean field equation ∆gu + ρ ( eu ∫ S2 e udμ − 1 4π ) = 0 in S2, where ρ is a real parameter. We obtain the existence of multiple axially asymmetric solutions bifurcating from u = 0 at the values ρ = 4n(n + 1)π for any odd integer n ≥ 3.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
