A note on uniqueness of the ground state for nonlinear Schrödinger equations. (October 2019)

• Record Type: Journal Article
• Authors: Mei, Xia; Tian, Shuying
• Is Part Of: Applied mathematics letters. Volume 96(2019)
• Page Start: 115
• Page End: 121
• Publication Date: 2019-10
• Subjects: Nonlinear Schrödinger equations -- Concentration -- Uniqueness -- Pohozaev identity; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.04.026
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We are concerned with the following nonlinear Schrödinger equation − ε 2 Δ u + V ( x ) u = | u | p − 2 u, u ∈ H 1 ( R N ), where N ≥ 3, 2 < p < 2 N N − 2 . For ε small enough and a class of V ( x ), we show the uniqueness of the positive ground state under certain assumptions on asymptotic behavior of V ( x ) and its first derivatives. Here our results are suitable for a kind of V ( x ) which has different increasing rates at different directions.