CONCENTRATION PHENOMENA FOR CRITICAL FRACTIONAL SCHRODINGER SYSTEMS

In this paper we study the existence, multiplicity and concentration behavior of solutions for the following critical fractional Schrodinger system {epsilon(2s)(-Delta)(s)u + V(x)u = Qu(u, v) + 1/2*(s) K-u(u, v) in R-N epsilon(2s)(-Delta)(s)u + W(x)v = Q(v)(u, v) + 1/2*(s) K-v(u, v) in R-N u, v > 0 in R-N, where epsilon > 0 is a parameter, s is an element of (0, 1), N > 2s, (-Delta)(s) is the fractional Laplacian operator, V : R-N -> R and W : R-N -> R are positive Holder continuous potentials, Q and K are homogeneous C-2-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.