Solutions to a class of singular quasilinear elliptic equations
Volume 98 / 2010
Annales Polonici Mathematici 98 (2010), 231-240
MSC: 35J05, 35J62.
DOI: 10.4064/ap98-3-3
Abstract
We study the existence of positive solutions to $$ \cases{\mathop{\rm div} ({|\nabla{u}|^{p-2} \nabla{u}})+q(x)u^{-{\gamma}}=0&\hbox{on }{\mit\Omega},\cr u=0&\hbox{on }\partial{\mit\Omega},} $$ where ${\mit\Omega}$ is $\mathbb{R}^N$ or an unbounded domain, $q(x)$ is locally Hölder continuous on ${\mit\Omega}$ and $ p>1$, $\gamma>-(p-1)$.
