Existence of solutions for a system with general Hardy–Sobolev singular criticalities Arroyo, Ángel López Soriano, Rafael Ortega, Alejandro 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. 2025-05-14T09:14:46Z 2025-05-14T09:14:46Z 2025-04-07 journal article Arroyo, Á., López-Soriano, R. & Ortega, A. Existence of solutions for a system with general Hardy–Sobolev singular criticalities. Calc. Var. 64, 131 (2025). [https://doi.org/10.1007/s00526-025-02990-y] https://hdl.handle.net/10481/104102 10.1007/s00526-025-02990-y eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer Nature