Existence of Positive Bounded Solutions of Semilinear Elliptic Problems
This paper is concerned with the existence of bounded positive solution for the semilinear elliptic problem Δu=λp(x)f(u) in Ω subject to some Dirichlet conditions, where Ω is a regular domain in ℝn (n≥3) with compact boundary. The nonlinearity f is nonnegative continuous and the potential p belongs...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2010/134078 |
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| _version_ | 1832551029674082304 |
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| author | Faten Toumi |
| author_facet | Faten Toumi |
| author_sort | Faten Toumi |
| collection | DOAJ |
| description | This paper is concerned with the existence of bounded positive solution for the semilinear elliptic problem Δu=λp(x)f(u) in Ω subject to some Dirichlet conditions, where Ω is a regular domain in ℝn (n≥3) with compact boundary. The nonlinearity f is nonnegative continuous and the potential p belongs to some Kato class K(Ω). So we prove the existence of a positive continuous solution depending on λ by the use of a potential theory approach. |
| format | Article |
| id | doaj-art-29f725bc75e14c46b9fefd430778a3f2 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-29f725bc75e14c46b9fefd430778a3f22025-02-03T06:05:09ZengWileyInternational Journal of Differential Equations1687-96431687-96512010-01-01201010.1155/2010/134078134078Existence of Positive Bounded Solutions of Semilinear Elliptic ProblemsFaten Toumi0Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, 2092 Tunis, TunisiaThis paper is concerned with the existence of bounded positive solution for the semilinear elliptic problem Δu=λp(x)f(u) in Ω subject to some Dirichlet conditions, where Ω is a regular domain in ℝn (n≥3) with compact boundary. The nonlinearity f is nonnegative continuous and the potential p belongs to some Kato class K(Ω). So we prove the existence of a positive continuous solution depending on λ by the use of a potential theory approach.http://dx.doi.org/10.1155/2010/134078 |
| spellingShingle | Faten Toumi Existence of Positive Bounded Solutions of Semilinear Elliptic Problems International Journal of Differential Equations |
| title | Existence of Positive Bounded Solutions of Semilinear Elliptic Problems |
| title_full | Existence of Positive Bounded Solutions of Semilinear Elliptic Problems |
| title_fullStr | Existence of Positive Bounded Solutions of Semilinear Elliptic Problems |
| title_full_unstemmed | Existence of Positive Bounded Solutions of Semilinear Elliptic Problems |
| title_short | Existence of Positive Bounded Solutions of Semilinear Elliptic Problems |
| title_sort | existence of positive bounded solutions of semilinear elliptic problems |
| url | http://dx.doi.org/10.1155/2010/134078 |
| work_keys_str_mv | AT fatentoumi existenceofpositiveboundedsolutionsofsemilinearellipticproblems |