A comparison principle for quasilinear elliptic equations (Q1374920)

The main result of this work is a comparison principle for sub- and supersolutions to equations of the form \[ \text{div}(|\nabla u|^{\alpha-2}\nabla u)=a|u|^q\text{ sgn }u, \qquad a>0, \quad q>0, \quad \alpha\geq 1,\tag{1} \] and to more general quasilinear divergence-type second-order elliptic equations that are considered in arbitrary domains of \(\mathbb{R}^n\), \(n\geq 2\).