Local uniqueness of multi-peak solutions to a class of Schrodinger equations with competing potential

作者：Niu, Yahui; Tian, Shuying; Yang, Pingping^*

来源：Journal of Mathematical Physics, 2023, 64(3): 031509.

DOI：10.1063/5.0134220

• SEMICLASSICAL BOUND-STATES
• POSITIVE SOLUTIONS
• EXISTENCE
• BUMP

In this paper, we consider the nonlinear Schrodinger equations. Let A(x) := [V(x)](p/p-2 - N2) [K(x)](- 2/p-2). Under some conditions on A, we show the local uniqueness of positive multi-peak solutions concentrating near k(k >= 2) distinct non-degenerate critical points of A by using the local Pohozaev identity. We generalize Cao-Li-Luo's results to the competing potential cases and show how these two potentials impact the uniqueness of concentrated solutions.

• 单位
  武汉理工大学; 郑州大学