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

2024/05/31 by Ángel Arroyo, Arroyo, Ángel, Rafael López-Soriano +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2405.20845

openalex publication_date 2024/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study a class of Hardy--Sobolev type systems defined in 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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