Mass concentration and uniqueness of ground states for mass subcritical rotational nonlinear Schrodinger equations

This paper considers ground states of mass subcritical rotational nonlinear Schrodinger equation-.6u + V(x)u + iQ(x perpendicular to center dot Vu) = mu u + rho p-1|u|p-1u in R2, where V(x) is an external potential, Q > 0 characterizes the rotational velocity of the trap V(x), 1 < p < 3, and rho > 0 describes the strength of the attractive interactions. It is shown that ground states of the above equation can be described equivalently by minimizers of the L2-constrained variational problem. We prove that minimizers exist for any rho E (0, oo) when 0 < Q < Q*, where 0 < Q* := Q*(V) < oo denotes the critical rotational velocity. While Q > Q*, there admits no minimizers for any rho E (0, oo). For fixed 0 < Q < Q*, by using energy estimates and blow-up analysis, we also analyze the mass concentration behavior of minimizers as rho-+ oo. Finally, we prove that up to a constant phase, there exists a unique minimizer when Q E (0, Q*) is fixed and rho > 0 is large enough.(c) 2023 Elsevier Ltd. All rights reserved.