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

In this paper we study a class of Hardy--Sobolev type systems defined in \(\mathbb{R}^N\) 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, w...

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Published in:arXiv.org 2024-05
Main Authors: Arroyo, Ángel, López-Soriano, Rafael, Ortega, Alejandro
Format: Article
Language:English
Subjects:
Critical point
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Summary:In this paper we study a class of Hardy--Sobolev type systems defined in \(\mathbb{R}^N\) 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.
ISSN:2331-8422