Correlation between two quasilinear elliptic problems with a source term involving the function or its gradient

Haydar Abdelhamid (1) , Marie-Françoise Bidaut-Véron (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

Thanks to a change of unknown we compare two elliptic quasilinear problems with Dirichlet data in a bounded domain of R^{N}. The first one, of the form -Δ_{p}u=β(u)|∇u|^{p}+λf(x), where β is nonnegative, involves a gradient term with natural growth. The second one, of the form -Δ_{p}v=λf(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.

Mots clés: Quasilinear elliptic equations; renormalized solutions; extremal solutions; measure data

Domaines: Equations aux dérivées partielles [math.AP]

Haydar Abdelhamid, Marie-Françoise Bidaut-Véron. Correlation between two quasilinear elliptic problems with a source term involving the function or its gradient. 2008. ⟨hal-00326563v1⟩