Revista Matemática Iberoamericana

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Volume 24, Issue 2, 2008, pp. 597–616
DOI: 10.4171/RMI/548

Published online: 2008-08-31

Quasilinear equations with natural growth

David Arcoya[1] and Pedro J. Martínez-Aparicio[2]

(1) Universidad de Granada, Spain
(2) Universidad de Granada, Spain

We study the existence of positive solution $w\in H_0^1(\Omega)$ of the quasilinear equation $-\Delta w+ g(w)|\nabla w|^2=a(x)$, $x\in \Omega$, where $\Omega$ is a bounded domain in $\mathbb R^N$, $0\leq a\in L^\infty (\Omega )$ and $g$ is a nonnegative continuous function on $(0,+\infty)$ which may have a singularity at zero.

Keywords: Quasilinear elliptic equations, critical growth, singular nonlinearity

Arcoya David, Martínez-Aparicio Pedro: Quasilinear equations with natural growth. Rev. Mat. Iberoam. 24 (2008), 597-616. doi: 10.4171/RMI/548