  We study properties of positive functions satisfying (E)
--$\Delta$u+m|$\nabla$u| q -- u p = 0 is a domain $\Omega$ or in R N + when p >
1 and 1 < q < 2. We give sufficient conditions for the existence of a solution
to (E) with a nonnegative measure $\mu$ as boundary data, and these conditions
are expressed in terms of Bessel capacities on the boundary. We also study
removable boundary singularities and solutions with an isolated singularity on
$\partial$$\Omega$. The different results depends on two critical exponents for
p = p c := N +1 N --1 and for q = q c := N +1 N and on the position of q with
respect to 2p p+1. Contents
