We study ground states of two-dimensional Bose–Einstein condensates with repulsive ( \(a\gt 0\) ) or attractive ( \(a\lt 0\) ) interactions in a trap \(V (x)\) rotating at velocity \(\Omega\) . It is known that there exist critical parameters \(a^{\ast }\gt 0\) and \(\Omega^{\ast }:=\Omega^{\ast }(V(x))\gt 0\) such that if \(\Omega \gt \Omega^{\ast }\) , then there is no ground state for any \(a\in \mathbb{R}\) ; if \(0\le \Omega \lt \Omega^{\ast }\) , then ground states exist if and only if \(a\in (-a^{\ast },+\infty )\) . As a completion of ...
