Existence of solutions for a system with general Hardy--Sobolev singular criticalities
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.20845
- arXiv:
- arXiv:2405.20845
- Bibcode:
- 2024arXiv240520845A
- Keywords:
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- Mathematics - Analysis of PDEs
- E-Print:
- arXiv admin note: text overlap with arXiv:2211.17047