Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian
The aim of this paper is to establish existence and uniqueness of a positive continuous solution to the following singular nonlinear problem. {-t1-ntn-1u′′=a(t)uσ, t∈(0,1), limt→0tn-1u′(t)=0, u(1)=0}, where n≥3,σ<1, and a denotes a nonnegative continuous function that might have the property...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/3572132 |
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| author | Imed Bachar Habib Mâagli Said Mesloub |
| author_facet | Imed Bachar Habib Mâagli Said Mesloub |
| author_sort | Imed Bachar |
| collection | DOAJ |
| description | The aim of this paper is to establish existence and uniqueness of a positive continuous solution to the following singular nonlinear problem. {-t1-ntn-1u′′=a(t)uσ, t∈(0,1), limt→0tn-1u′(t)=0, u(1)=0}, where n≥3,σ<1, and a denotes a nonnegative continuous function that might have the property of being singular at t=0 and /or t=1 and which satisfies certain condition associated to Karamata class. We emphasize that the nonlinearity might also be singular at u=0, while the solution could blow-up at 0. Our method is based on the global estimates of potential functions and the Schauder fixed point theorem. |
| format | Article |
| id | doaj-art-3b3fa5e0af744cf9b744e3f58c6e47e0 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-3b3fa5e0af744cf9b744e3f58c6e47e02025-02-03T06:11:06ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/35721323572132Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial LaplacianImed Bachar0Habib Mâagli1Said Mesloub2King Saud University, College of Science, Mathematics Department, P.O. Box 2455, Riyadh 11451, Saudi ArabiaKing Abdulaziz University, College of Sciences and Arts, Rabigh Campus, Department of Mathematics, P. O. Box 344, Rabigh 21911, Saudi ArabiaKing Saud University, College of Science, Mathematics Department, P.O. Box 2455, Riyadh 11451, Saudi ArabiaThe aim of this paper is to establish existence and uniqueness of a positive continuous solution to the following singular nonlinear problem. {-t1-ntn-1u′′=a(t)uσ, t∈(0,1), limt→0tn-1u′(t)=0, u(1)=0}, where n≥3,σ<1, and a denotes a nonnegative continuous function that might have the property of being singular at t=0 and /or t=1 and which satisfies certain condition associated to Karamata class. We emphasize that the nonlinearity might also be singular at u=0, while the solution could blow-up at 0. Our method is based on the global estimates of potential functions and the Schauder fixed point theorem.http://dx.doi.org/10.1155/2019/3572132 |
| spellingShingle | Imed Bachar Habib Mâagli Said Mesloub Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian Journal of Function Spaces |
| title | Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian |
| title_full | Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian |
| title_fullStr | Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian |
| title_full_unstemmed | Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian |
| title_short | Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian |
| title_sort | existence and global asymptotic behavior of singular positive solutions for radial laplacian |
| url | http://dx.doi.org/10.1155/2019/3572132 |
| work_keys_str_mv | AT imedbachar existenceandglobalasymptoticbehaviorofsingularpositivesolutionsforradiallaplacian AT habibmaagli existenceandglobalasymptoticbehaviorofsingularpositivesolutionsforradiallaplacian AT saidmesloub existenceandglobalasymptoticbehaviorofsingularpositivesolutionsforradiallaplacian |