Effect of the Domain Geometry on the Solutions to Fractional Brezis-Nirenberg Problem
In this paper, we consider the Brezis-Nirenberg problem for the nonlocal fractional elliptic equation Aαux=NN-2αuxp+εux, x∈Ω, ux>0, x∈Ω, u(x)=0, x∈∂Ω, where 0<α<1 is fixed, p=N+2α/N-2α, ε is a small parameter, and Ω is a bounded smooth domain of RN(N≥4α). Aα denotes the fractional Laplace o...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/1093804 |
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| author | Qiaoyu Tian Yonglin Xu |
| author_facet | Qiaoyu Tian Yonglin Xu |
| author_sort | Qiaoyu Tian |
| collection | DOAJ |
| description | In this paper, we consider the Brezis-Nirenberg problem for the nonlocal fractional elliptic equation Aαux=NN-2αuxp+εux, x∈Ω, ux>0, x∈Ω, u(x)=0, x∈∂Ω, where 0<α<1 is fixed, p=N+2α/N-2α, ε is a small parameter, and Ω is a bounded smooth domain of RN(N≥4α). Aα denotes the fractional Laplace operator defined through the spectral decomposition. Under some geometry hypothesis on the domain Ω, we show that all solutions to this problem are least energy solutions. |
| format | Article |
| id | doaj-art-eebb970791b0470faebfe1a2126ef36e |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-eebb970791b0470faebfe1a2126ef36e2025-02-03T06:15:11ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/10938041093804Effect of the Domain Geometry on the Solutions to Fractional Brezis-Nirenberg ProblemQiaoyu Tian0Yonglin Xu1School of Mathematics and Computer, Northwest Minzu University, Lanzhou, Gansu 730000, ChinaSchool of Mathematics and Computer, Northwest Minzu University, Lanzhou, Gansu 730000, ChinaIn this paper, we consider the Brezis-Nirenberg problem for the nonlocal fractional elliptic equation Aαux=NN-2αuxp+εux, x∈Ω, ux>0, x∈Ω, u(x)=0, x∈∂Ω, where 0<α<1 is fixed, p=N+2α/N-2α, ε is a small parameter, and Ω is a bounded smooth domain of RN(N≥4α). Aα denotes the fractional Laplace operator defined through the spectral decomposition. Under some geometry hypothesis on the domain Ω, we show that all solutions to this problem are least energy solutions.http://dx.doi.org/10.1155/2019/1093804 |
| spellingShingle | Qiaoyu Tian Yonglin Xu Effect of the Domain Geometry on the Solutions to Fractional Brezis-Nirenberg Problem Journal of Function Spaces |
| title | Effect of the Domain Geometry on the Solutions to Fractional Brezis-Nirenberg Problem |
| title_full | Effect of the Domain Geometry on the Solutions to Fractional Brezis-Nirenberg Problem |
| title_fullStr | Effect of the Domain Geometry on the Solutions to Fractional Brezis-Nirenberg Problem |
| title_full_unstemmed | Effect of the Domain Geometry on the Solutions to Fractional Brezis-Nirenberg Problem |
| title_short | Effect of the Domain Geometry on the Solutions to Fractional Brezis-Nirenberg Problem |
| title_sort | effect of the domain geometry on the solutions to fractional brezis nirenberg problem |
| url | http://dx.doi.org/10.1155/2019/1093804 |
| work_keys_str_mv | AT qiaoyutian effectofthedomaingeometryonthesolutionstofractionalbrezisnirenbergproblem AT yonglinxu effectofthedomaingeometryonthesolutionstofractionalbrezisnirenbergproblem |