Abstract
We consider the semiclassical asymptotic behaviors of ground state solution for the following two‐component Hartree system: urn:x-wiley:mma:media:mma5820:mma5820-math-0001 which is originated from the study on cold atoms of boson and fermion system with long‐range interaction. Under the assumption urn:x-wiley:mma:media:mma5820:mma5820-math-0002 by detailed compactness analysis, we prove that there is a β0>0 such that if β<β0, the system has a ground state solution. For this solution, the energy estimates and the decay rates are presented, and the asymptotic profiles as ε→0 are displayed in details for β<0 and β>0, respectively. Furthermore, we show that for β<0, the phase separation phenomenon may occur.
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