On a nonlocal elliptic system of Hardy‐Kirchhoff type with critical exponents

Abstract

In this work, we consider a class of critical variational systems in of the Hardy‐Kirchhoff type involving the fractional Laplacian operator. By imposing some conditions on the nonlinearity as well as in the potencial, we recover the compactness combining arguments used in Alves and Souto and in Brezis and Nirenberg. Only monotonicity conditions are employed, without imposing any coercivity condition on the potential, which can tend to zero at infinity. Our result is closely related to that obtained by Fiscella, Pucci and Zhang.