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arXiv · 0810.0897

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

Haydar Abdelhamid·Marie-Françoise Bidaut-Véron
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Abstract

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 $-Δ_{p}u=β(u)| \nabla u| ^{p}+λf(x),$ 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.

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Haydar Abdelhamid, Marie-Françoise Bidaut-Véron. 2008-11-20. Correlation between two quasilinear elliptic problems with a source term involving the function or its gradient. https://arxiv.org/abs/0810.0897

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