Work

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

Year: 2025

Type: article

Abstract: In this paper we study a class of Hardy–Sobolev type systems defined in $$\mathbb {R}^N$$ 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.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-025-02990-y

Authors: Ángel Arroyo, Rafael López-Soriano, Alejandro Ortega

Institutions: University of Alicante, Universidad de Granada, Universidad Nacional de Educación a Distancia

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: European Commission, Universidad de Granada, Agencia Estatal de Investigación, NextGenerationEU