A remark on quasilinear Schrödinger equations with Berestycki–Lions conditions. (June 2021)

• Record Type: Journal Article
• Authors: Chen, Jianhua; Cheng, Bitao; Hu, Jiangong
• Is Part Of: Applied mathematics letters. Volume 116(2021)
• Publication Date: 2021-06
• Subjects: Quasilinear Schrödinger equation -- Nonexistence -- Ground state solutions -- Berestycki–Lions conditions; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107038
• Languages: English
• ISSNs: 0893-9659

Abstract

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 ) .