Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity

Abstract

This paper focuses on the following scalar field equation involving a fractional Laplacian: where N ⩾ 2, α ∈ (0, 1), (−Δ)α stands for the fractional Laplacian. Using some minimax arguments, we obtain a positive ground state under the general Berestycki–Lions type assumptions.