Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity
We study the following semilinear biharmonic equation , which satisfies 0<u̲λ<1. In the extremal case λ=λ*, we prove the existence of a weak solution which is the unique solution even in a very weak sense. Besides, several new difficulties arise and many problems still remain to be solved. We...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/896902 |
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| _version_ | 1832549870573977600 |
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| author | Baishun Lai |
| author_facet | Baishun Lai |
| author_sort | Baishun Lai |
| collection | DOAJ |
| description | We study the following semilinear biharmonic equation , which satisfies 0<u̲λ<1. In the extremal case λ=λ*, we prove the existence of a weak solution which is the unique solution even in a very weak sense. Besides, several new difficulties arise and many problems still remain to be solved. We list those of particular interest in the final section. |
| format | Article |
| id | doaj-art-9bf042516ab049619311e64e1c1d925f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9bf042516ab049619311e64e1c1d925f2025-02-03T06:08:26ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/896902896902Some Remarks on Biharmonic Elliptic Problems with a Singular NonlinearityBaishun Lai0Institute of Contemporary Mathematics, Henan University, Kaifeng 475004, ChinaWe study the following semilinear biharmonic equation , which satisfies 0<u̲λ<1. In the extremal case λ=λ*, we prove the existence of a weak solution which is the unique solution even in a very weak sense. Besides, several new difficulties arise and many problems still remain to be solved. We list those of particular interest in the final section.http://dx.doi.org/10.1155/2014/896902 |
| spellingShingle | Baishun Lai Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity Abstract and Applied Analysis |
| title | Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity |
| title_full | Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity |
| title_fullStr | Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity |
| title_full_unstemmed | Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity |
| title_short | Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity |
| title_sort | some remarks on biharmonic elliptic problems with a singular nonlinearity |
| url | http://dx.doi.org/10.1155/2014/896902 |
| work_keys_str_mv | AT baishunlai someremarksonbiharmonicellipticproblemswithasingularnonlinearity |