Ground states for fractional Schrödinger equations involving a critical nonlinearity

This paper is aimed to study ground states for a class of fractional Schrödinger equations involving the critical exponents: (-Δ)^α u + u = λf(u) + |u|^{2α ∗ - 2}u in ℝ^N, where λ is a real parameter, (-Δ)^α is the fractional Laplacian operator with 0 < α < 1, 2_α ^∗ = 2N/N - 2α 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.