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This work deals with a family of Hardy-Sobolev doubly critical system definedin $\mathbb{R}^n$. More precisely, we provide a classification of the positivesolutions, whose expressions comprise multiplies of solutions of the decoupledscalar equation. Our strategy is based on the symmetry of the solutions,deduced via a suitable version of the moving planes technique for cooperativesingular systems, joint with the study of the asymptotic behavior by using theMoser's iteration scheme.

Classification of solutions to Hardy-Sobolev Doubly Critical Systems