Abstract

We study properties of positive functions satisfying (E) - Delta u + u(p) - M vertical bar del u vertical bar(q) = 0 is a domain Omega or in R-+(N) when p > 1 and 1 < q < min{p, 2}. We concentrate our research on the solutions of (E) vanishing on the boundary except at one point. This analysis depends on the existence of separable solutions in R-+(N). We construct various types of positive solutions with an isolated singularity on the boundary. We also study conditions for the removability of compact boundary sets and the Dirichlet problem associated to (E) with a measure as boundary data.