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Existence of critical elliptic systems with boundary singularities

Yang J., Zhou Y.

Opuscula Mathematica

2013

Vol. 33, no. 2

373--390

In this paper, we are concerned with the existence of positive solutions of the following nonlinear elliptic system involving critical Hardy-Sobolev exponent [formula] where N ≥4 and Ω is a C1 bounded domain in RN with [formula].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.