Multiple solutions for a critical fractional elliptic system involving concave-convex nonlinearities

We are concerned with the multiplicity of solutions to the system driven by a fractional operator with homogeneous Dirichlet boundary conditions. Namely, using fibering maps and the Nehari manifold, we obtain multiple solutions to the following fractional elliptic system: (-Delta)(s)u = lambda vertical bar u vertical bar(q-2)u + 2 alpha/alpha + beta vertical bar u vertical bar alpha-2u vertical bar v vertical bar beta in Omega, (-Delta)(s)v = mu vertical bar v vertical bar(q-2)v + 2 beta/alpha + beta vertical bar u vertical bar(alpha)vertical bar v vertical bar(beta-2)v in Omega, u - v - 0 in R-n \ Omega, where Omega is a smooth bounded set in R-n, n > 2s, with s is an element of (0, 1); (-Delta)(s) is the fractional Laplace operator;, lambda, mu > 0 are two parameters; the exponent n/(n - 2s) <= q < 2; a > 1, beta > 1 satisfy 2 < alpha + beta = 2(s)*; 2(s)(*) = 2n/(n - 2s) (n > 2s) is the fractional critical Sobolev exponent.