The Brezis–Nirenberg problem for fractional systems with Hardy potentials

Abstract

In this work, we study the existence of positive solutions to the following fractional elliptic systems with Hardy‐type singular potentials and coupled by critical homogeneous nonlinearities where (− Δ)s denotes the fractional Laplace operator, is a smooth bounded domain such that 0 ∈ Ω, μ1, μ2 ∈ [0, ΛN, s) with ΛN, s the sharp constant of the fractional Hardy inequality, and is the fractional critical Sobolev exponent. In order to prove the main result, we study the related fractional Hardy–Sobolev type inequalities and then establish the existence of positive solutions to the systems through variational methods.