A remark on quasilinear Schrödinger equations with Berestycki–Lions conditions. (June 2021) - Chen, Jianhua; Cheng, Bitao; Hu, Jiangong
Abstract: In this paper, we study the quasilinear Schrödinger 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 superlinear and asymptotically linear case. Unlike V ∈ C 2 ( R N, R ), we only need to assume that V ∈ C 1 ( R N, R ) .