Boundary singularities of semilinear elliptic equations with Leray-Hardy potential.

We study existence and uniqueness of solutions of ( E 1 ) − Δ 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 ). [ABSTRACT FROM AUTHOR]