Ground states for fractional Schrödinger equations with critical growth.

In this paper, we study the following critical fractional Schrödinger equation: ( − Δ ) s u + V ( x ) u = | u | 2 s * − 2 u + λ f ( x , u ) , x ∈ R N , where <italic>λ</italic> > 0, 0 < <italic>s</italic> < 1, <italic>N</italic> > 2<italic>s</italic>, 2 s * = 2 N N − 2 s , (−Δ)<italic>s</italic> denotes the fractional Laplacian of order <italic>s</italic>, and <italic>f</italic> is a continuous superlinear but subcritical function. When <italic>V</italic> and <italic>f</italic> are asymptotically periodic in <italic>x</italic>, we prove that the equation has a ground state solution for large <italic>λ</italic> by the Nehari method. [ABSTRACT FROM AUTHOR]