The Solvability of Fractional Elliptic Equation with the Hardy Potential
In this paper, we study the existence and nonexistence of solutions to fractional elliptic equations with the Hardy potential −Δsu−λu/x2s=ur−1+δgu,in Ω,ux>0,in Ω,ux=0,in ℝN∖Ω, where Ω⊂ℝN is a bounded Lipschitz domain with 0∈Ω, −Δs is a fractional Laplace operator, s∈0,1, N>2s, δ is a positive...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/5414309 |
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| author | Siyu Gao Shuibo Huang Qiaoyu Tian Zhan-Ping Ma |
| author_facet | Siyu Gao Shuibo Huang Qiaoyu Tian Zhan-Ping Ma |
| author_sort | Siyu Gao |
| collection | DOAJ |
| description | In this paper, we study the existence and nonexistence of solutions to fractional elliptic equations with the Hardy potential −Δsu−λu/x2s=ur−1+δgu,in Ω,ux>0,in Ω,ux=0,in ℝN∖Ω, where Ω⊂ℝN is a bounded Lipschitz domain with 0∈Ω, −Δs is a fractional Laplace operator, s∈0,1, N>2s, δ is a positive number, 2<r<rλ,s≡N+2s−2αλ/N−2s−2αλ+1, αλ∈0,N−2s/2 is a parameter depending on λ, 0<λ<ΛN,s, and ΛN,s=22sΓ2N+2s/4/Γ2N−2s/4 is the sharp constant of the Hardy–Sobolev inequality. |
| format | Article |
| id | doaj-art-2f7abd6abe6c418eb53b3c7376ae6323 |
| institution | OA Journals |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-2f7abd6abe6c418eb53b3c7376ae63232025-08-20T02:08:11ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/54143095414309The Solvability of Fractional Elliptic Equation with the Hardy PotentialSiyu Gao0Shuibo Huang1Qiaoyu Tian2Zhan-Ping Ma3School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou, Gansu 730030, ChinaSchool of Mathematics and Computer Science, Northwest Minzu University, Lanzhou, Gansu 730030, ChinaSchool of Mathematics and Computer Science, Northwest Minzu University, Lanzhou, Gansu 730030, ChinaSchool of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454003, ChinaIn this paper, we study the existence and nonexistence of solutions to fractional elliptic equations with the Hardy potential −Δsu−λu/x2s=ur−1+δgu,in Ω,ux>0,in Ω,ux=0,in ℝN∖Ω, where Ω⊂ℝN is a bounded Lipschitz domain with 0∈Ω, −Δs is a fractional Laplace operator, s∈0,1, N>2s, δ is a positive number, 2<r<rλ,s≡N+2s−2αλ/N−2s−2αλ+1, αλ∈0,N−2s/2 is a parameter depending on λ, 0<λ<ΛN,s, and ΛN,s=22sΓ2N+2s/4/Γ2N−2s/4 is the sharp constant of the Hardy–Sobolev inequality.http://dx.doi.org/10.1155/2020/5414309 |
| spellingShingle | Siyu Gao Shuibo Huang Qiaoyu Tian Zhan-Ping Ma The Solvability of Fractional Elliptic Equation with the Hardy Potential Complexity |
| title | The Solvability of Fractional Elliptic Equation with the Hardy Potential |
| title_full | The Solvability of Fractional Elliptic Equation with the Hardy Potential |
| title_fullStr | The Solvability of Fractional Elliptic Equation with the Hardy Potential |
| title_full_unstemmed | The Solvability of Fractional Elliptic Equation with the Hardy Potential |
| title_short | The Solvability of Fractional Elliptic Equation with the Hardy Potential |
| title_sort | solvability of fractional elliptic equation with the hardy potential |
| url | http://dx.doi.org/10.1155/2020/5414309 |
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