Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball
Here we study the polyharmonic nonlinear elliptic boundary value problem on the unit ball B in ℝn(n≥2)(−△)mu+g(⋅,u)=0, in B (in the sense of distributions) limx→ξ∈∂B(u(x)/(1−|x|2)m−1)=0(ξ). Under appropriate conditions related to a Kato class on the nonlinearity g(x,t), we give some existence result...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2007/56981 |
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| _version_ | 1832568251320631296 |
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| author | Sonia Ben Othman Habib Mâagli Malek Zribi |
| author_facet | Sonia Ben Othman Habib Mâagli Malek Zribi |
| author_sort | Sonia Ben Othman |
| collection | DOAJ |
| description | Here we study the polyharmonic nonlinear elliptic
boundary value problem on the unit ball B in ℝn(n≥2)(−△)mu+g(⋅,u)=0, in B (in the sense of distributions)
limx→ξ∈∂B(u(x)/(1−|x|2)m−1)=0(ξ). Under appropriate conditions related to a Kato class on the nonlinearity
g(x,t), we give some existence results. Our approach is based on estimates for the polyharmonic Green function
on B with zero Dirichlet boundary conditions, including a 3G-theorem,
which leeds to some useful properties on functions belonging to the Kato class. |
| format | Article |
| id | doaj-art-d9b898fec70d43d6a3907c0b22a78ab5 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d9b898fec70d43d6a3907c0b22a78ab52025-02-03T00:59:30ZengWileyAbstract and Applied Analysis1085-33751687-04092007-01-01200710.1155/2007/5698156981Existence Results for Polyharmonic Boundary Value Problems in the Unit BallSonia Ben Othman0Habib Mâagli1Malek Zribi2Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 2092, TunisiaDépartement de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 2092, TunisiaDépartement de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 2092, TunisiaHere we study the polyharmonic nonlinear elliptic boundary value problem on the unit ball B in ℝn(n≥2)(−△)mu+g(⋅,u)=0, in B (in the sense of distributions) limx→ξ∈∂B(u(x)/(1−|x|2)m−1)=0(ξ). Under appropriate conditions related to a Kato class on the nonlinearity g(x,t), we give some existence results. Our approach is based on estimates for the polyharmonic Green function on B with zero Dirichlet boundary conditions, including a 3G-theorem, which leeds to some useful properties on functions belonging to the Kato class.http://dx.doi.org/10.1155/2007/56981 |
| spellingShingle | Sonia Ben Othman Habib Mâagli Malek Zribi Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball Abstract and Applied Analysis |
| title | Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball |
| title_full | Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball |
| title_fullStr | Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball |
| title_full_unstemmed | Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball |
| title_short | Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball |
| title_sort | existence results for polyharmonic boundary value problems in the unit ball |
| url | http://dx.doi.org/10.1155/2007/56981 |
| work_keys_str_mv | AT soniabenothman existenceresultsforpolyharmonicboundaryvalueproblemsintheunitball AT habibmaagli existenceresultsforpolyharmonicboundaryvalueproblemsintheunitball AT malekzribi existenceresultsforpolyharmonicboundaryvalueproblemsintheunitball |