Estimates for the Green function and singular solutions for polyharmonic nonlinear equation
We establish a new form of the 3G theorem for polyharmonic Green function on the unit ball of ℝn(n≥2) corresponding to zero Dirichlet boundary conditions. This enables us to introduce a new class of functions Km,n containing properly the classical Kato class Kn. We exploit properties of functions be...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503209039 |
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| _version_ | 1832565755646836736 |
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| author | Imed Bachar Habib Màagli Syrine Masmoudi Malek Zribi |
| author_facet | Imed Bachar Habib Màagli Syrine Masmoudi Malek Zribi |
| author_sort | Imed Bachar |
| collection | DOAJ |
| description | We establish a new form of the 3G theorem for polyharmonic Green function on the unit ball of ℝn(n≥2) corresponding to zero Dirichlet boundary conditions. This enables us to introduce a new class of functions Km,n containing properly the classical Kato class Kn. We exploit properties of functions belonging to Km,n to prove an infinite existence result of singular positive solutions for nonlinear elliptic equation of order 2m. |
| format | Article |
| id | doaj-art-ee7d626ef7594851a3c3fa52bbf35b4e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ee7d626ef7594851a3c3fa52bbf35b4e2025-02-03T01:06:54ZengWileyAbstract and Applied Analysis1085-33751687-04092003-01-0120031271574110.1155/S1085337503209039Estimates for the Green function and singular solutions for polyharmonic nonlinear equationImed Bachar0Habib Màagli1Syrine Masmoudi2Malek Zribi3Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 1060, TunisiaDépartement de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 1060, TunisiaDépartement de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 1060, TunisiaDépartement de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 1060, TunisiaWe establish a new form of the 3G theorem for polyharmonic Green function on the unit ball of ℝn(n≥2) corresponding to zero Dirichlet boundary conditions. This enables us to introduce a new class of functions Km,n containing properly the classical Kato class Kn. We exploit properties of functions belonging to Km,n to prove an infinite existence result of singular positive solutions for nonlinear elliptic equation of order 2m.http://dx.doi.org/10.1155/S1085337503209039 |
| spellingShingle | Imed Bachar Habib Màagli Syrine Masmoudi Malek Zribi Estimates for the Green function and singular solutions for polyharmonic nonlinear equation Abstract and Applied Analysis |
| title | Estimates for the Green function and singular solutions for polyharmonic nonlinear equation |
| title_full | Estimates for the Green function and singular solutions for polyharmonic nonlinear equation |
| title_fullStr | Estimates for the Green function and singular solutions for polyharmonic nonlinear equation |
| title_full_unstemmed | Estimates for the Green function and singular solutions for polyharmonic nonlinear equation |
| title_short | Estimates for the Green function and singular solutions for polyharmonic nonlinear equation |
| title_sort | estimates for the green function and singular solutions for polyharmonic nonlinear equation |
| url | http://dx.doi.org/10.1155/S1085337503209039 |
| work_keys_str_mv | AT imedbachar estimatesforthegreenfunctionandsingularsolutionsforpolyharmonicnonlinearequation AT habibmaagli estimatesforthegreenfunctionandsingularsolutionsforpolyharmonicnonlinearequation AT syrinemasmoudi estimatesforthegreenfunctionandsingularsolutionsforpolyharmonicnonlinearequation AT malekzribi estimatesforthegreenfunctionandsingularsolutionsforpolyharmonicnonlinearequation |