Existence results for a fractional elliptic system with critical Sobolev‐Hardy exponents and concave‐convex nonlinearities

Abstract

In this paper, we study the following nonlinear fractional Laplacian system with critical Sobolev‐Hardy exponent where is a smooth bounded domain in , , , , , , satisfy , is the critical Sobolev‐Hardy exponent, , are parameters, , and are nonnegative functions on . Using the variational methods and analytic techniques, we prove that the critical fractional Laplacian system admits at least two positive solutions when the pair of parameters belongs to a suitable subset of .