The ground state of two coupled Gross-Pitaevskii equations in the   Thomas-Fermi limit
  We prove existence and uniqueness of a positive solution to a system of two coupled Gross-Pitaevskii equations. We give a full asymptotic expansion of this solution into powers of the semi classical parameter $\varepsilon$ in the Thomas--Fermi limit $\varepsilon\to 0$. 
Clement Gallo
math.AP