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

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

2008-10-06

arxiv.org/abs/0810.0897v2

Mathematics

Analysis of PDEs

Scientific paper

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 $-\Delta_{p}u=\beta(u)| \nabla u| ^{p}+\lambda f(x),$ 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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