Abstract

In the present paper, we study the existence of nonnegative solutions to the Dirichlet problem Lp,qM u: = -Δ u+up-M|∇u|q=μ in a domain ω ∈ RN where μ is a nonnegative Radon measure, when p>1, q>1 and M≥0. We also give conditions under which nonnegative solutions of Lp,qM u=0 in ω\K, where K is a compact subset of ω, can be extended as a solution of the same equation in ω.