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arXiv · 2405.20845

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

Ángel Arroyo·Rafael López-Soriano·Alejandro Ortega
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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.

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Ángel Arroyo, Rafael López-Soriano, Alejandro Ortega. 2024-05-31. Existence of solutions for a system with general Hardy--Sobolev singular criticalities. https://arxiv.org/abs/2405.20845

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