A note on uniqueness of the ground state for nonlinear Schrödinger equations. (October 2019) - Mei, Xia; Tian, Shuying
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.