Weak solutions of semilinear elliptic equations with Leray-Hardy potentials and measure data

We study existence and stability of solutions of -Delta u + mu/vertical bar x vertical bar(2)u + gu = nu in Omega, u = 0 on partial derivative Omega, where Omega is a bounded, smooth domain of R-N , N >= 2, containing the origin, mu >= - (N-2)/4(2) is a constant, g is a nondecreasing function satisfying some integral growth assumption and the weak Delta(2)-condition, and v is a Radon measure in Omega. We show that the situation differs depending on whether the measure is diffuse or concentrated at the origin. When g is a power function, we introduce a capacity framework to find necessary and sufficient conditions for solvability.