On the Existence of Positive Solutions of a Nonlinear Differential Equation
We study some existence results for the nonlinear equation (1/A)(Au')'=uψ(x,u) for x∈(0,ω) with different boundary conditions, where ω∈(0,∞], A is a continuous function on [0,ω), positive and differentiable on (0,ω), and ψ is a nonnegative function on (0,ω)×[0,∞) such that t↦tψ(x,t) is con...
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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: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/58658 |
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| _version_ | 1832568335151136768 |
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| author | Sonia Ben Othman Habib Mâagli Noureddine Zeddini |
| author_facet | Sonia Ben Othman Habib Mâagli Noureddine Zeddini |
| author_sort | Sonia Ben Othman |
| collection | DOAJ |
| description | We study some existence results for the nonlinear
equation (1/A)(Au')'=uψ(x,u) for x∈(0,ω) with different boundary conditions, where ω∈(0,∞],
A is a continuous function on [0,ω), positive and differentiable on (0,ω), and ψ is a nonnegative function on (0,ω)×[0,∞) such that t↦tψ(x,t) is continuous on [0,∞) for each x∈(0,ω). We give asymptotic behavior for positive solutions using a potential theory approach. |
| format | Article |
| id | doaj-art-0eebf9f17d0b4e82b7a1feb648b939c5 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0eebf9f17d0b4e82b7a1feb648b939c52025-02-03T00:59:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/5865858658On the Existence of Positive Solutions of a Nonlinear Differential EquationSonia Ben Othman0Habib Mâagli1Noureddine Zeddini2Département 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, TunisiaWe study some existence results for the nonlinear equation (1/A)(Au')'=uψ(x,u) for x∈(0,ω) with different boundary conditions, where ω∈(0,∞], A is a continuous function on [0,ω), positive and differentiable on (0,ω), and ψ is a nonnegative function on (0,ω)×[0,∞) such that t↦tψ(x,t) is continuous on [0,∞) for each x∈(0,ω). We give asymptotic behavior for positive solutions using a potential theory approach.http://dx.doi.org/10.1155/2007/58658 |
| spellingShingle | Sonia Ben Othman Habib Mâagli Noureddine Zeddini On the Existence of Positive Solutions of a Nonlinear Differential Equation International Journal of Mathematics and Mathematical Sciences |
| title | On the Existence of Positive Solutions of a Nonlinear Differential Equation |
| title_full | On the Existence of Positive Solutions of a Nonlinear Differential Equation |
| title_fullStr | On the Existence of Positive Solutions of a Nonlinear Differential Equation |
| title_full_unstemmed | On the Existence of Positive Solutions of a Nonlinear Differential Equation |
| title_short | On the Existence of Positive Solutions of a Nonlinear Differential Equation |
| title_sort | on the existence of positive solutions of a nonlinear differential equation |
| url | http://dx.doi.org/10.1155/2007/58658 |
| work_keys_str_mv | AT soniabenothman ontheexistenceofpositivesolutionsofanonlineardifferentialequation AT habibmaagli ontheexistenceofpositivesolutionsofanonlineardifferentialequation AT noureddinezeddini ontheexistenceofpositivesolutionsofanonlineardifferentialequation |