On the Fractional Schrodinger Equations with Critical Nonlinearity

In this paper, we study the existence and multiplicity results for the following critical fractional Schrodinger equation with magnetic field epsilon(2)s(-delta)(s)(A/epsilon)q + V(x)q-lambda f(|q|)q- K(x)|q|(2 & lowast;)(s) (-2)q = 0, in R-N, where epsilon > 0, lambda > 0, s is an element of (0, 1), N >= 3, 2(s)(& lowast;) = 2N/N-2s , V : R-N -> R and A : R-N -> R-N are the electric and magnetic potentials respectively. The methods used here are based on the Nehari manifold method, Ekeland's variational principle and the Ljusternick-Schnirelmann category theory.