Lions-type theorem of the fractional Laplacian and applications

In this paper, our goal is to establish a generalized version of Lions-type theorem for the fractional Laplacian. As an application of this theorem, we consider the existence of ground state solutions of a fractional equation:\[(-Δ)^s u + V ( x ) u = f(u), \; x ∈ R^N ,\]where N 3, s ∈ (1/2, 1), V is a singular potential with α ∈ (0, 2s) ∪ (2s, 2N - 2s), and the nonlinearity f has the critical growth, discussed without any boundary value condition.