Existence and local uniqueness of normalized solutions for two-component Bose-Einstein condensates

作者：Guo, Qing; Xie, Huafei^*

来源：Zeitschrift für Angewandte Mathematik und Physik, 2021, 72(6): 189.

DOI：10.1007/s00033-021-01619-2

• Normalized solution
• Local Pohozaev identities
• Local uniqueness
• Excited states
• Bose-Einstein condensates

In this paper, we consider the following two-component Bose-Einstein condensates (BEC) @@@ {-Delta u(1) + V-1(x)u(1) = a(1)u(1)(3) + mu u(1) + beta u(1)u(2)(2) in R-2, -Delta u(2) + V-2(x)u(2) = a(2)u(2)(3) + mu u(2) + beta u(1)(2)u(2) in R-2, @@@ with the constraint integral(R2)(u(1)(2) + u(2)(2))dx = 1. The existence and local uniqueness of k-peak solutions are given by finite-dimensional reduction and local Pohozaev identities, which gives the description of excited state of BEC phenomenon stated and generalizes the results in [15] about the ground states.