The Nehari manifold for fractional systems involving critical nonlinearities

We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents. With the help of the Nehari manifold, we prove that the system admits at least two positive solutions when the pair of parameters $(\lambda ,\mu )$ belongs to a suitable subset of ${\mathbb{R}}^2$.