Quasilinear elliptic equations with singular quadratic growth terms

Abstract

In this paper we deal with positive solutions for singular quasilinear problems whose model is $$ \begin{cases} -Δu + \frac{|\nabla u|^2}{(1-u)^γ}=g & \mbox{in $Ω$,}\newline \hfill u=0 \hfill & \mbox{on $\partialΩ$,} \end{cases} $$ where $\Omega$ is a bounded open set of ${\mathbb{R}}^N$, $g\ge 0$ is a function in some Lebesgue space, and $\gamma >0$. We prove both existence and nonexistence of solutions depending on the value of $\gamma$ and on the size of $g$.

References in corpus (2)

• Inverse Problem for a Curved Quantum Guide
• Existence and nonexistence of solutions for singular quadratic quasilinear equations

Cited by in corpus (1)

• A generalized porous medium equation related to some singular quasilinear problems