{"title":"三维临界非局部问题的正基态解","authors":"X. Qian","doi":"10.4208/jpde.v35.n4.6","DOIUrl":null,"url":null,"abstract":". In this paper, we are interested in the following nonlocal problem with critical exponent where a , b are positive constants, 2 < p < 6, Ω is a smooth bounded domain in R 3 and λ > 0 is a parameter. By variational methods, we prove that problem has a positive ground state solution u b for λ > 0 sufficiently large. Moreover, we take b as a parameter and study the asymptotic behavior of u b when b ց 0.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"47 2 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Positive Ground State Solutions for a Critical Nonlocal Problem in Dimension Three\",\"authors\":\"X. Qian\",\"doi\":\"10.4208/jpde.v35.n4.6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In this paper, we are interested in the following nonlocal problem with critical exponent where a , b are positive constants, 2 < p < 6, Ω is a smooth bounded domain in R 3 and λ > 0 is a parameter. By variational methods, we prove that problem has a positive ground state solution u b for λ > 0 sufficiently large. Moreover, we take b as a parameter and study the asymptotic behavior of u b when b ց 0.\",\"PeriodicalId\":43504,\"journal\":{\"name\":\"Journal of Partial Differential Equations\",\"volume\":\"47 2 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Partial Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4208/jpde.v35.n4.6\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Partial Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/jpde.v35.n4.6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Positive Ground State Solutions for a Critical Nonlocal Problem in Dimension Three
. In this paper, we are interested in the following nonlocal problem with critical exponent where a , b are positive constants, 2 < p < 6, Ω is a smooth bounded domain in R 3 and λ > 0 is a parameter. By variational methods, we prove that problem has a positive ground state solution u b for λ > 0 sufficiently large. Moreover, we take b as a parameter and study the asymptotic behavior of u b when b ց 0.
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