{"title":"非线性分数阶Neumann椭圆方程正解的存在性","authors":"Haoqi Ni, Aliang Xia, Xiongjun Zheng","doi":"10.7153/DEA-2018-10-07","DOIUrl":null,"url":null,"abstract":"This article is devoted to study the fractional Neumann elliptic problem ⎧⎪⎨ ⎪⎩ ε2s(−Δ)su+u = up in Ω, ∂νu = 0 on ∂Ω, u > 0 in Ω, where Ω is a smooth bounded domain of RN , N > 2s , 0 < s s0 < 1 , 1 < p < (N +2s)/(N− 2s) , ε > 0 and ν is the outer normal to ∂Ω . We show that there exists at least one nonconstant solution uε to this problem provided ε is small. Moreover, we prove that uε ∈ L∞(Ω) by using Moser-Nash iteration.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"26 1","pages":"115-129"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Existence of positive solutions for nonlinear fractional Neumann elliptic equations\",\"authors\":\"Haoqi Ni, Aliang Xia, Xiongjun Zheng\",\"doi\":\"10.7153/DEA-2018-10-07\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This article is devoted to study the fractional Neumann elliptic problem ⎧⎪⎨ ⎪⎩ ε2s(−Δ)su+u = up in Ω, ∂νu = 0 on ∂Ω, u > 0 in Ω, where Ω is a smooth bounded domain of RN , N > 2s , 0 < s s0 < 1 , 1 < p < (N +2s)/(N− 2s) , ε > 0 and ν is the outer normal to ∂Ω . We show that there exists at least one nonconstant solution uε to this problem provided ε is small. Moreover, we prove that uε ∈ L∞(Ω) by using Moser-Nash iteration.\",\"PeriodicalId\":11162,\"journal\":{\"name\":\"Differential Equations and Applications\",\"volume\":\"26 1\",\"pages\":\"115-129\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/DEA-2018-10-07\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/DEA-2018-10-07","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Existence of positive solutions for nonlinear fractional Neumann elliptic equations
This article is devoted to study the fractional Neumann elliptic problem ⎧⎪⎨ ⎪⎩ ε2s(−Δ)su+u = up in Ω, ∂νu = 0 on ∂Ω, u > 0 in Ω, where Ω is a smooth bounded domain of RN , N > 2s , 0 < s s0 < 1 , 1 < p < (N +2s)/(N− 2s) , ε > 0 and ν is the outer normal to ∂Ω . We show that there exists at least one nonconstant solution uε to this problem provided ε is small. Moreover, we prove that uε ∈ L∞(Ω) by using Moser-Nash iteration.
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