Boundary Singularities of Solutions to Semilinear Fractional Equations
We prove the existence of a solution of (-Δ)su+f(u)=0{(-\Delta)^{s}u+f(u)=0} in a smooth bounded domain Ω with a prescribed boundary value μ in the class of Radon measures for a large class of continuous functions f satisfying a weak singularity condition expressed under an integral form. We study...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-04-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2017-6048 |
| _version_ | 1828118740213956608 |
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| author | Nguyen Phuoc-Tai Véron Laurent |
| author_facet | Nguyen Phuoc-Tai Véron Laurent |
| author_sort | Nguyen Phuoc-Tai |
| collection | DOAJ |
| description | We prove the existence of a solution of (-Δ)su+f(u)=0{(-\Delta)^{s}u+f(u)=0} in a smooth bounded domain Ω with a prescribed boundary value μ in the class of Radon measures for a large class of continuous functions f satisfying a weak singularity condition expressed under an integral form. We study the existence of a boundary trace for positive moderate solutions. In the particular case where f(u)=up{f(u)=u^{p}} and μ is a Dirac mass, we show the existence of several critical exponents p. We also demonstrate the existence of several types of separable solutions of the equation (-Δ)su+up=0{(-\Delta)^{s}u+u^{p}=0} in ℝ+N{\mathbb{R}^{N}_{+}}. |
| first_indexed | 2024-04-11T13:37:35Z |
| format | Article |
| id | doaj.art-5c3164a8fe8d463cbe977205931621fa |
| institution | Directory Open Access Journal |
| issn | 1536-1365 2169-0375 |
| language | English |
| last_indexed | 2024-04-11T13:37:35Z |
| publishDate | 2018-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-5c3164a8fe8d463cbe977205931621fa2022-12-22T04:21:24ZengDe GruyterAdvanced Nonlinear Studies1536-13652169-03752018-04-0118223726710.1515/ans-2017-6048Boundary Singularities of Solutions to Semilinear Fractional EquationsNguyen Phuoc-Tai0Véron Laurent1Department of Mathematics and Statistics, Masaryk University, 611 37Brno, Czech RepublicLaboratoire de Mathématiques et Physique Théorique, Faculté des Sciences, Université François Rabelais, 37200Tours, FranceWe prove the existence of a solution of (-Δ)su+f(u)=0{(-\Delta)^{s}u+f(u)=0} in a smooth bounded domain Ω with a prescribed boundary value μ in the class of Radon measures for a large class of continuous functions f satisfying a weak singularity condition expressed under an integral form. We study the existence of a boundary trace for positive moderate solutions. In the particular case where f(u)=up{f(u)=u^{p}} and μ is a Dirac mass, we show the existence of several critical exponents p. We also demonstrate the existence of several types of separable solutions of the equation (-Δ)su+up=0{(-\Delta)^{s}u+u^{p}=0} in ℝ+N{\mathbb{R}^{N}_{+}}.https://doi.org/10.1515/ans-2017-6048semilinear fractional equationsboundary trace35j66 35j67 35r06 35r11 |
| spellingShingle | Nguyen Phuoc-Tai Véron Laurent Boundary Singularities of Solutions to Semilinear Fractional Equations Advanced Nonlinear Studies semilinear fractional equations boundary trace 35j66 35j67 35r06 35r11 |
| title | Boundary Singularities of Solutions to Semilinear Fractional Equations |
| title_full | Boundary Singularities of Solutions to Semilinear Fractional Equations |
| title_fullStr | Boundary Singularities of Solutions to Semilinear Fractional Equations |
| title_full_unstemmed | Boundary Singularities of Solutions to Semilinear Fractional Equations |
| title_short | Boundary Singularities of Solutions to Semilinear Fractional Equations |
| title_sort | boundary singularities of solutions to semilinear fractional equations |
| topic | semilinear fractional equations boundary trace 35j66 35j67 35r06 35r11 |
| url | https://doi.org/10.1515/ans-2017-6048 |
| work_keys_str_mv | AT nguyenphuoctai boundarysingularitiesofsolutionstosemilinearfractionalequations AT veronlaurent boundarysingularitiesofsolutionstosemilinearfractionalequations |