Ground states for fractional Schrodinger equations involving a critical nonlinearity

This paper is aimed to study ground states for a class of fractional Schrodinger equations involving the critical exponents: (-Delta)(alpha)u + u = lambda f(u) + vertical bar u vertical bar 2(a)*-2(u) in IRN, where lambda is a real parameter, (-Delta)(alpha) is the fractional Laplacian operator with 0 < a < 1, 2(a)* = 2N/N-2 alpha, with 2 <= N, f is a continuous subcritical nonlinearity without the Ambrosetti-Rabinowitz condition. Based on the principle of concentration compactness in the fractional Sobolev space and radially decreasing rearrangements, we obtain a nonnegative radially symmetric minimizer for a constrained minimization problem which has the least energy among all possible solutions for the above equations, i.e., a ground state solution.