Partial Differential Equations
Correlation between two quasilinear elliptic problems with a source term involving the function or its gradient
Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1251-1256.

Thanks to a change of unknown we compare two elliptic quasilinear problems with Dirichlet data in a bounded domain of RN. The first one, of the form Δpu=β(u)|u|p+λf(x), where β is nonnegative, involves a gradient term with natural growth. The second one, of the form Δpv=λf(x)(1+g(v))p1 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.

A l'aide d'un changement d'inconnue nous comparons deux problèmes elliptiques quasilinéaires avec conditions de Dirichlet dans un domaine borné Ω de RN. Le premier, de la forme Δpu=β(u)|u|p+λf(x), où β est positif, comporte un terme de gradient à croissance critique. Le second, de la forme Δpv=λf(x)(1+g(v))p1g est croissante, contient un terme de source d'ordre 0. La comparaison donne des résultats nouveaux d'existence, nonexistence et multiplicité pour les deux problèmes.

Received:
Published online:
DOI: 10.1016/j.crma.2008.10.002
Hamid, Haydar Abdel 1; Bidaut-Véron, Marie Françoise 1

1 Laboratoire de mathématiques et physique théorique, CNRS UMR 6083, faculté des sciences, 37200 Tours, France
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Hamid, Haydar Abdel; Bidaut-Véron, Marie Françoise. Correlation between two quasilinear elliptic problems with a source term involving the function or its gradient. Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1251-1256. doi : 10.1016/j.crma.2008.10.002. http://www.numdam.org/articles/10.1016/j.crma.2008.10.002/

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