We study existence and uniqueness of solutions of (E 1) −∆u + µ |x| ^{-2} u + g(u) = ν in Ω, u = λ on ∂Ω, where Ω ⊂ R N + is a bounded smooth domain such that 0 ∈ ∂Ω, µ ≥ − N 2 4 is a constant, g a continuous nondecreasing function satisfying some integral growth condition and ν and λ two Radon measures respectively in Ω and on ∂Ω. We show that the situation differs considerably according the measure is concentrated at 0 or not. When g is a power we introduce a capacity framework which provides necessary and sufficient conditions for the solvability of problem (E 1).