Concentration phenomena for critical fractional Schrödinger systems

In this paper we study the existence, multiplicity and concentration behavior of solutions for the following critical fractional Schrödinger system s e e u,2 2 s sv((- ->?) ?) 0s s u u + + V W ((x x ) ) u v = = Q Q u v ((u, u, v v ) ) + + 221 1 ** _K K u v ((u, u, v v ) ) in in R R N N s in RN, where e > 0 is a parameter, s ? (0, 1), N > 2s, (-?)s is the fractional Laplacian operator, V : RN ? R and W : RN ? R are positive Hölder continuous potentials, Q and K are homogeneous C2-functions having subcritical and critical growth respectively. We relate the number of solutions with the topology of the set where the potentials V and W attain their minimum values. The proofs rely on the Ljusternik-Schnirelmann theory and variational methods.