Existence of critical elliptic systems with boundary singularities

Abstract

Abstract. In this paper, we are concerned with the existence of positive solutions of the following nonlinear elliptic system involving critical Hardy-Sobolev exponentwhere N ≥ 4 and Ω is a C 1 bounded domain in R N with 0 ∈ ∂Ω. 0 < s < 2, α + β = 2, α, β > 1, λ > 0 and 1 < p <. The case when 0 belongs to the boundary of Ω is closely related to the mean curvature at the origin on the boundary. We show in this paper that problem ( * ) possesses at least a positive solution.