Boundary singular problems for quasilinear equations involving mixed reaction-diffusion (Q6585724)

This article is concerned with the study of the equation \(-\Delta u+u^p-M|\nabla u|^q=0\) in a \(C^2\)-bounded domain of \(\mathbb{R}^N\), \(p>1\), \(1<q<2\), \(M>0\). The solutions of the equation are assumed to satisfy one of the following conditions at the boundary: either \(u=\mu\) on \(\partial\Omega\), where \(\mu\geq 0\) is a Radon measure; or \(u=0\) on \(\partial\Omega\setminus\{a\}\), where \(a\in \partial\Omega\) is an isolated boundary singularity. Capacitary conditions are determined for the existence of a solution in case of data measure on the boundary, while removability of the singularity in the second case are discussed.