Boundary singularities of semilinear elliptic equations with Leray-Hardy potential

Abstract

We study existence and uniqueness of solutions of ([Formula: see text]) [Formula: see text] in [Formula: see text], [Formula: see text] on [Formula: see text], where [Formula: see text] is a bounded smooth domain such that [Formula: see text], [Formula: see text] is a constant, [Formula: see text] a continuous nondecreasing function satisfying some integral growth condition and [Formula: see text] and [Formula: see text] two Radon measures, respectively, in [Formula: see text] and on [Formula: see text]. We show that the situation differs considerably according the measure is concentrated at [Formula: see text] or not. When [Formula: see text] is a power we introduce a capacity framework which provides necessary and sufficient conditions for the solvability of problem ([Formula: see text]).