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

In this paper, we study the following nonlinear fractional Laplacian system with critical Sobolev-Hardy exponent (Formula presented.) where (Formula presented.) is a smooth bounded domain in (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.) satisfy (Formula presented.), (Formula presented.) is the critical Sobolev-Hardy exponent, (Formula presented.), (Formula presented.) are parameters, (Formula presented.), (Formula presented.) and (Formula presented.) are nonnegative functions on (Formula presented.). 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 (Formula presented.) belongs to a suitable subset of (Formula presented.).