Local uniqueness of ground states for rotating bose-einstein condensates with attractive interactions

Authors：Guo, Yujin; Luo, Yong; Peng, Shuangjie^*

Source：Calculus of Variations and Partial Differential Equations, 2021, 60(6): 237.

DOI：10.1007/s00526-021-02055-w

• NONLINEAR SCHRODINGER-EQUATIONS
• BOUND-STATES
• MULTI-BUMP
• STABILITY
• EXISTENCE
• VORTICES
• COLLAPSE
• GAS

We study ground states of two-dimensional Bose-Einstein condensates with attractive interactions in a trap V(x) rotating at the velocity Omega. It is known that there exists a critical rotational velocity 0 < Omega* := Omega* (V)<=infinity and a critical number 0 < a* < infinity such that for any rotational velocity 0 <= Omega < Omega*, ground states exist if and only if the coupling constant a satisfies a < a *. For a general class of traps V(x), which may not be symmetric, we prove in this paper that up to a constant phase, there exists a unique ground state as a NE arrow a*, where Omega is an element of (0, Omega*) is fixed.