Quasilinear elliptic equations with singular quadratic growth terms

2025/08/11 by Boccardo, Lucio, Leonori, Tommaso, Orsina, Luigi +1
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.07695

Abstract

In this paper we deal with positive solutions for singular quasilinear problems whose model is \begincases -Δu + (|∇ u|²)/((1-u)^γ)=g amp; in Ω,\newline \hfill u=0 \hfill amp; on ∂Ω, \endcases where Ω is a bounded open set of ℝ^N, g≥ 0 is a function in some Lebesgue space, and γ>0. We prove both existence and nonexistence of solutions depending on the value of γ and on the size of g.

Citations

• Existence and nonexistence of solutions for singular quadratic quasilinear equations
• Correlation between two quasilinear elliptic problems with a source term involving the function or its gradient

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