Existence of solutions for a system with general Hardy–Sobolev singular criticalities

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In this paper we study a class of Hardy–Sobolev type systems defined in RN and coupled by a singular critical Hardy–Sobolev term. The main novelty of this work is that the orders of the singularities are independent and contained in a wide range. By means of variational techniques, we will prove the existence of positive bound and ground states for such a system. In particular, we find solutions as minimizers or Mountain–Pass critical points of the energy functional on the underlying Nehari manifold.