In this paper, we study the existence and uniqueness of positive solutions for the following nonlinear fractional elliptic equation: (-Delta)(alpha)u = lambda alpha(x)u - b(x)u(p) in R-N, where alpha is an element of (0, 1), N >= 2, lambda > 0, alpha and b are positive smooth function in R-N satisfying a(x) -> a(infinity) > 0 and b(x) -> b(infinity) > 0 as vertical bar x vertical bar -> infinity. Our proof is based on a comparison principle and existence, uniqueness and asymptotic behaviors of various boundary blow-up solutions for a class of elliptic equations involving the fractional Laplacian.Regular 2015FONDECYTFONDECYT