A remark on quasilinear Schrödinger equations with Berestycki-Lions conditions

Abstract In this paper, we study the quasilinear Schrodinger equation − Δ u + V ( x ) u − Δ ( u 2 ) u = g ( u ) , x ∈ R N , where N ≥ 3 , 2 ∗ = 2 N N − 2 , V ( x ) is a potential function. By using a change of variable, we prove the non-existence of ground state solutions with Berestycki-Lions conditions, which contain the superliner and asymptotically linear case. Unlike V ∈ C 2 ( R N , R ) , we only need to assume that V ∈ C 1 ( R N , R ) .