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

2008/10/06 by Abdelhamid, Haydar, Bidaut-Véron, Marie-Françoise · 2 citations
#35J60 #35J70 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0810.0897

Abstract

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_pu=β(u)| ∇ u| ^p+λf(x), where β is nonnegative, involves a gradient term with natural growth. The second one, of the form -Δ_pv=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.

Cited by

• Existence and a priori bounds for fully nonlinear PDEs with a harmonic map-like structure
• Quasilinear elliptic equations with singular quadratic growth terms

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