Concentration Phenomena for Fractional Elliptic Equations Involving Exponential Critical Growth

In this paper, we deal with the singular perturbed fractional elliptic problem is an element of(-Delta)(1/2)u + V(z)u = f(u) in IR, where (-Delta)(1/)2u is the square root of the Laplacian and f(s) has exponential critical growth. Under suitable conditions on f(s), we construct a localized bound state solution concentrating at an isolated component of the positive local minimum points of the potential of V as epsilon goes to 0.