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| HAL : hal-00326563, version 2 |
| arXiv : 0810.0897 |
| Fiche détaillée |  Récupérer au format |
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| Comptes Rendus de l Académie des Sciences - Series I - Mathematics 346 (2008) 1251-1256 |
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| Versions disponibles : | v1 (06-10-2008) | v2 (20-11-2008) |
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| Correlation between two quasilinear elliptic problems with a source term involving the function or its gradient |
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| Haydar Abdelhamid 1Marie-Françoise Bidaut-Véron 1 |
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| (05/10/2008) |
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| Thanks to a change of unknown we compare two elliptic quasilinear problems with Dirichlet data in a bounded domain of $\mathbb{R}^{N}.$ The first one, of the form $-\Delta_{p}u=\beta(u)\left\vert \nabla u\right\vert ^{p}+\lambda f(x),$ where $\beta$ is nonnegative, involves a gradient term with natural growth. The second one, of the form $-\Delta_{p}v=\lambda f(x)(1+g(v))^{p-1}$ where $g$ is nondecreasing, presents a source term of order $0$. The correlation gives new results of existence, nonexistence and multiplicity for the two problems. |
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| 1 : | Laboratoire de Mathématiques et Physique Théorique (LMPT) |
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CNRS : UMR6083 – Université François Rabelais - Tours |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Quasilinear elliptic equations – renormalized solutions – extremal solutions – measure data |
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| hal-00326563, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00326563 | |
| oai:hal.archives-ouvertes.fr:hal-00326563 | |
| Contributeur : Marie-Françoise Bidaut-Véron | |
| Soumis le : Mercredi 19 Novembre 2008, 11:36:59 | |
| Dernière modification le : Jeudi 12 Février 2009, 17:47:48 | |
