Existence of solutions for a system with general Hardy--Sobolev singular criticalities
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916267537989632 |
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| author | Arroyo, Ángel López-Soriano, Rafael Ortega, Alejandro |
| author_facet | Arroyo, Ángel López-Soriano, Rafael Ortega, Alejandro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20845 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of solutions for a system with general Hardy--Sobolev singular criticalities Arroyo, Ángel López-Soriano, Rafael Ortega, Alejandro Analysis of PDEs 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. |
| title | Existence of solutions for a system with general Hardy--Sobolev singular criticalities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.20845 |