Nonlinear elliptic systems involving Hardy-Sobolev Criticalities

2022/11/30 by Rafael López-Soriano, López-Soriano, Rafael, Alejandro Ortega +1
Engineering · Mathematics · #35J47 #35J50 #35J60 #35Q40 (Primary) #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2211.17047

openalex publication_date 2022/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This paper is focused on the solvability of a family of nonlinear elliptic systems defined in ℝ^N. Such equations contain Hardy potentials and Hardy-Sobolev criticalities coupled by a possible critical Hardy-Sobolev term. That problem arises as a generalization of Gross-Pitaevskii and Bose-Einstein type systems. By means of variational techniques, we shall find ground and bound states in terms of the coupling parameter ν and the order of the different parameters and exponents. In particular, for a wide range of parameters we find solutions as minimizers or Mountain-Pass critical points of the energy functional on the underlying Nehari manifold.

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