Singularly Perturbed Fractional Schrodinger Equations with Critical Growth

We are concerned with the following singularly perturbed fractional Schrodinger equation: {epsilon(2s)(-Delta)(s)u + V(x)u = f(u) in R-N, u is an element of H-s(R-N), u > 0 on R-N, where epsilon is a small positive parameter, N > 2s, and (-Delta)(5), with s is an element of(0, 1), is the fractional Laplacian. Using variational technique, we construct a family of positive solutions u(epsilon) is an element of H-s(R-N) which concentrates around the local minima of V as epsilon -> 0 under general conditions on f which we believe to be almost optimal.